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GELE Mathematics — Advanced Engineering MathematicsMemory Anchors

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Quick-recall memory tricks for GELE Mathematics — Advanced Engineering Mathematics. Acronyms, rhymes, visual hooks, and association techniques that turn rote memorisation into reliable recall. Built specifically for the concepts Professional Regulation Commission (PRC) — Board of Geodetic Engineering tests most often.

Exam context

Professional Regulation Commission (PRC) — Board of Geodetic Engineering runs the Geodetic Engineer Licensure Examination on September 2026. Its Mathematics section sits under a "Core" weighting, and Advanced Engineering Mathematics is the 8th chapter in the 10-chapter GELE Mathematics rotation. The GELE passing mark is 70% weighted average, no sub-test below 50%, and the most recent 2026 paper drew about a meaningful share of questions from Mathematics.

Advanced Engineering Mathematics - Memory Anchors

Memory techniques can increase retention by up to 400% compared to passive re-reading. For the PRC Civil Engineer board exam, where Advanced Engineering Mathematics covers complex numbers, matrices, determinants, Cramer's rule, and vectors, you cannot afford to blank out on formulas under pressure. This collection uses mnemonics, vivid analogies, micro-stories, visual associations, and rhymes — all scientifically proven to encode information into long-term memory. Each anchor is tied to a specific concept so that when you see a board question, the right formula fires instantly. Filipino cultural references are woven in to make the anchors more personal and stickier. Study these actively: say them aloud, sketch them, and test yourself with the recall triggers. The goal is zero hesitation on exam day.

Anchors

Topic

Complex Numbers

Concept

Complex number rectangular form: z = a + bi

Anchor Id

Difficulty

easy

Memory Aid

Think of a complex number like your LRT/MRT coordinates in Metro Manila. The 'a' is how far East-West you are (the real part, the x-axis), and 'b' is how far North-South (the imaginary part, the y-axis). You always need BOTH coordinates to find your exact station on the map — just like you need both 'a' and 'b' to fully describe the complex number. 'i' is just the label saying 'this is the North-South direction.'

Anchor Type

analogy

Why It Works

Spatial/geographic analogy anchors abstract algebraic concepts to a familiar real-world navigation system that Filipino students use daily, making the rectangular form intuitive.

Example Usage

When asked to identify the real and imaginary parts of z = 5 - 3i, recall the MRT map: real part = 5 (East-West), imaginary part = -3 (South direction on the North-South axis).

Recall Trigger

Imagine plotting your location on an MRT map.

Topic

Complex Numbers

Concept

Magnitude of a complex number: |z| = sqrt(a² + b²)

Anchor Id

Difficulty

easy

Memory Aid

The magnitude is the DIAGONAL of the right triangle formed by 'a' and 'b'. Remember it as the 'hypotenuse of the complex triangle' — it is pure Pythagorean theorem. Imagine you are in Binondo and you need to walk 3 blocks East and 4 blocks North to reach a restaurant. The shortest straight-line distance (the diagonal shortcut through the alley) is sqrt(3² + 4²) = 5 blocks. That shortcut distance IS the magnitude.

Anchor Type

analogy

Why It Works

Pythagorean theorem is deeply ingrained. Linking |z| to a familiar diagonal-shortcut scenario makes it effortless to recall the formula without confusion.

Example Usage

For z = 3 + 4i: |z| = sqrt(9 + 16) = sqrt(25) = 5. Immediately picture the 3-4-5 right triangle.

Recall Trigger

Think: diagonal shortcut in Binondo — Pythagorean theorem.

Topic

Complex Numbers

Concept

Argument (angle) of complex number: θ = arctan(b/a)

Anchor Id

Difficulty

medium

Memory Aid

Remember: 'B over A gives the angle, not A over B — Blame the Bottom!' The argument is arctan(IMAGINARY / REAL) = arctan(b/a). The mnemonic is 'ImagineRealAngle' → IRA → I over R → b/a. Also remember the QUADRANT CHECK with 'CAST rule': All positive in Q1, Sine positive in Q2, Tangent positive in Q3, Cosine positive in Q4. When 'a' is negative (left side), add 180° to the basic arctan result.

Anchor Type

mnemonic

Why It Works

The acronym IRA (Imaginary over Real gives Angle) provides a single word trigger. The CAST rule is a standard memory tool for quadrant sign checks.

Example Usage

For z = -3 + 4i: basic arctan(4/3) = 53.13°. But 'a' is negative (Q2), so θ = 180° - 53.13° = 126.87°.

Recall Trigger

IRA — Imaginary over Real = Angle. Then do CAST for quadrant.

Topic

Complex Numbers

Concept

De Moivre's Theorem: z^n = r^n ∠ nθ

Anchor Id

Difficulty

medium

Memory Aid

To the power of n? Here is what you do: RAISE the radius, MULTIPLY the angle too! r to the n, theta times n — De Moivre makes powers easy, do it again! Rhyme: 'Raise the r, spin the θ, multiply n and you are done today!'

Anchor Type

rhyme

Why It Works

A rhyme encodes the two operations (raise magnitude to n, multiply angle by n) into a rhythmic pattern that is hard to forget and easy to recall under exam pressure.

Example Usage

Compute (2∠30°)^4: r^4 = 2^4 = 16, angle = 4 × 30° = 120°. Answer: 16∠120°.

Recall Trigger

Raise the r, spin the θ — De Moivre!

Topic

Complex Numbers

Concept

nth Roots of a complex number: z^(1/n) = r^(1/n) ∠ [(θ + 360°k)/n], k = 0,1,...,n-1

Anchor Id

Difficulty

hard

Memory Aid

Imagine a pizza (the complex number) cut into n equal slices. The first slice starts at angle θ/n. Each next slice is exactly 360°/n further around the pizza. There are exactly n slices (roots). The radius of each slice tip is r^(1/n) — the nth root of the original distance. So: 'Take the nth root of the radius, divide the angle by n, then space n equally-separated roots around the circle, each 360°/n apart.'

Anchor Type

micro_story

Why It Works

The pizza slice analogy perfectly captures the equal angular spacing (360°/n) and the n distinct roots. Visual and tactile memory for the periodicity of roots.

Example Usage

Find the 4 fourth roots of 16∠0°: r^(1/4) = 2, angles = 0°/4 + 360°k/4 = 0°, 90°, 180°, 270°. Roots: 2∠0°, 2∠90°, 2∠180°, 2∠270°.

Recall Trigger

Pizza cut into n equal slices, each 360°/n apart, radius = r^(1/n).

Topic

Complex Numbers

Concept

Polar multiplication: multiply magnitudes, ADD angles

Anchor Id

Difficulty

easy

Memory Aid

Think of two jeepney trips. Trip 1: 3 km at bearing 20°. Trip 2: 4 km at bearing 30°. When you multiply complex numbers in polar form, you combine the DISTANCES (×) and the DIRECTIONS (+). The jeepney's total 'stretch' is the product of lengths; the total 'spin' is the sum of angles. Never add lengths AND add angles — that would be two separate trips to the same jeep terminal!

Anchor Type

analogy

Why It Works

The jeepney analogy separates the two distinct operations (× for magnitudes, + for angles) using a culturally familiar vehicle scenario, preventing the common error of adding magnitudes.

Example Usage

Multiply (3∠20°)(4∠30°) = (3×4)∠(20°+30°) = 12∠50°.

Recall Trigger

Jeepney multiplication: TIMES the distance, PLUS the direction.

Topic

Matrices and Determinants

Concept

2×2 Determinant: det = ad - bc

Anchor Id

Difficulty

easy

Memory Aid

Draw the 2×2 matrix. Now draw two DIAGONALS: one going down-right (a to d) — that is the POSITIVE diagonal. One going down-left (b to c) — that is the NEGATIVE diagonal. The determinant is POSITIVE diagonal MINUS NEGATIVE diagonal = ad - bc. Visualize it as an X shape: the \ diagonal is PLUS, the / diagonal is MINUS. Remember: 'Backslash earns cash (positive), Forward slash loses cash (negative).'

Anchor Type

visual_association

Why It Works

The visual X-shape with the backslash/forward-slash memory trick creates a strong visual-spatial memory. The cash analogy adds emotional tagging.

Example Usage

det [[2,3],[1,4]] = (2)(4) - (3)(1) = 8 - 3 = 5. Trace the backslash: 2→4 = +8. Trace forward slash: 3→1 = -3.

Recall Trigger

Draw an X on the 2×2 matrix. Backslash = +, Forward slash = -.

Topic

Matrices and Determinants

Concept

Matrix multiplication order: (m×n)(n×p) = (m×p); AB ≠ BA

Anchor Id

Difficulty

medium

Memory Aid

Remember 'INNER MATCH, OUTER RESULT': For (m×n)(n×p), the INNER dimensions (n and n) must MATCH, and the result is the OUTER dimensions (m×p). Think of it like two jeepney routes connecting: Route A goes m stops to n stops. Route B continues from n stops to p stops. They connect at n. The combined trip goes from m to p. AND — you cannot reverse jeepney routes: AB ≠ BA (you cannot go from p back to m the same way).

Anchor Type

mnemonic

Why It Works

The 'inner match, outer result' phrase is a classic and compact mnemonic that directly encodes the rule. The non-commutativity is reinforced by the one-way jeepney direction.

Example Usage

Can we multiply (3×2)(2×4)? Inner: 2 and 2 → MATCH. Result: 3×4 matrix. Can we do (2×4)(3×2)? Inner: 4 and 3 → NO MATCH. Cannot multiply.

Recall Trigger

INNER MATCH → OUTER RESULT. Jeepney routes are one-way.

Topic

Matrices and Determinants

Concept

2×2 Matrix Inverse: A⁻¹ = (1/det A) × [[d,-b],[-c,a]]

Anchor Id

Difficulty

medium

Memory Aid

For matrix [[a,b],[c,d]], the inverse follows the 'SWAP and SIGN' rule: SWAP a and d (they exchange positions on the main diagonal), put NEGATIVE SIGNS on b and c (they stay in place but flip sign). Then divide the whole thing by det A. Remember as: 'Swap the corners, Negate the sides, Divide by det — now you have the inverse!' Acronym: SND — Swap, Negate, Divide.

Anchor Type

mnemonic

Why It Works

The SND acronym is a 3-step procedural memory that orders the operations correctly and prevents the common error of negating the wrong elements.

Example Usage

Find A⁻¹ for [[1,2],[3,5]]: det = 5-6 = -1. Swap: d=5, a=1. Negate: -b=-2, -c=-3. A⁻¹ = (1/-1)[[5,-2],[-3,1]] = [[-5,2],[3,-1]].

Recall Trigger

SND: Swap corners, Negate sides, Divide by det.

Topic

Cramer's Rule

Concept

Cramer's Rule: xᵢ = det(Aᵢ) / det(A)

Anchor Id

A10

Difficulty

medium

Memory Aid

Imagine det(A) as the 'master key' to the whole system. Each unknown (x₁, x₂, ...) gets its own 'room key' — that is det(Aᵢ), where the i-th column of A is replaced by the answer column b. To open the door (find the unknown), you use the room key divided by the master key: xᵢ = det(Aᵢ) / det(A). If the master key is ZERO (det A = 0), no door opens — no unique solution exists! Board exam alert: always check det(A) first before applying Cramer's rule.

Anchor Type

micro_story

Why It Works

The master key / room key metaphor creates a hierarchical memory structure: det(A) as the gatekeeper and det(Aᵢ) as the specific key. The zero-determinant warning is embedded in the story.

Example Usage

System: 2x+3y=8, x+4y=9. det(A)=5 (master key). For x: replace column 1 with [8,9]: det=32-27=5. x=5/5=1. For y: replace column 2 with [8,9]: det=18-8=10. y=10/5=2.

Recall Trigger

Master key = det(A). Room key for xᵢ = det(Aᵢ). xᵢ = room key ÷ master key.

Topic

Cramer's Rule

Concept

Cramer's Rule: replace the i-th COLUMN (not row) with vector b

Anchor Id

A11

Difficulty

medium

Memory Aid

Remember 'COLUMN Cramer, not ROW Cramer' — the C in Cramer stands for COLUMN. When forming Aᵢ, you slide the b-vector INTO the i-th COLUMN slot. Think of it as a 'column swap' — only the column corresponding to the unknown changes. If you ever feel tempted to replace a row, remember: Cramer = Column, and 'C-C-C' — Cramer Changes Columns.

Anchor Type

mnemonic

Why It Works

The alliteration 'Cramer Changes Columns' (CCC) is a powerful phonetic anchor that prevents the extremely common error of replacing a row instead of a column.

Example Usage

For the 2nd unknown y in a 2×2 system, replace the 2nd COLUMN of A with b. Never replace the 2nd row.

Recall Trigger

CCC — Cramer Changes Columns only!

Topic

Vectors

Concept

Dot product formula: a·b = axbx + ayby + azbz = |a||b|cosθ

Anchor Id

A12

Difficulty

easy

Memory Aid

The dot product measures HOW MUCH two vectors agree in direction — like measuring how much two team members are walking toward the same goal. If they are perfectly aligned (same direction, θ = 0°), cos(0°) = 1 → maximum agreement. If they are perpendicular (θ = 90°), cos(90°) = 0 → zero agreement — they are working in completely different directions. If they are opposite (θ = 180°), cos(180°) = -1 → maximum disagreement. Board rule: 'Dot product ZERO means perpendicular!'

Anchor Type

analogy

Why It Works

The 'team agreement' analogy gives physical meaning to a formula that otherwise seems abstract. The three special-case values (0°, 90°, 180°) are automatically remembered through the analogy.

Example Usage

Are vectors a=(1,0,0) and b=(0,1,0) perpendicular? a·b = (1)(0)+(0)(1)+(0)(0) = 0. Yes, they are perpendicular (cosθ = 0, θ = 90°).

Recall Trigger

How much do the vectors agree? Dot product = agreement meter. Zero = perpendicular.

Topic

Vectors

Concept

Cross product result is PERPENDICULAR to both vectors; magnitude = |a||b|sinθ

Anchor Id

A13

Difficulty

medium

Memory Aid

Visualize the cross product using your RIGHT HAND (Right-Hand Rule). Point your fingers along vector a. Curl them toward vector b. Your THUMB points in the direction of a×b — which is perpendicular to BOTH a and b. The magnitude |a||b|sinθ equals the AREA OF THE PARALLELOGRAM formed by the two vectors. Memory: 'Cross means area, perpendicular, and right-hand rule.' If θ = 0° (parallel vectors), sin(0°) = 0 → cross product = zero vector.

Anchor Type

visual_association

Why It Works

The right-hand rule is a kinesthetic memory — using your physical hand creates a bodily memory that is extremely robust. The parallelogram area connection gives geometric meaning.

Example Usage

For a=(1,0,0) and b=(1,0,0) (parallel): |a×b| = |1||1|sin(0°) = 0. Cross product is zero — confirms parallel vectors.

Recall Trigger

Right hand! Fingers = a, curl to b, thumb = a×b direction. Magnitude = parallelogram area.

Topic

Vectors

Concept

Cross product computation via 3×3 determinant with i, j, k

Anchor Id

A14

Difficulty

hard

Memory Aid

Remember the COFACTOR EXPANSION along the first row of: [[i,j,k],[ax,ay,az],[bx,by,bz]]. The trick: 'i POSITIVE, j NEGATIVE, k POSITIVE' — alternating signs in the first row! Mnemonic: 'I Just Kidding' — I(+), J(-), K(+). Expand each: i-component = (ay·bz - az·by), j-component = -(ax·bz - az·bx), k-component = (ax·by - ay·bx). The middle term ALWAYS gets the negative sign — the j-hat is the 'black sheep' with the minus.

Anchor Type

mnemonic

Why It Works

The phrase 'I Just Kidding' encodes the alternating +/-/+ signs for i/j/k expansion. The 'black sheep j' gives a vivid image for the minus sign on the middle component.

Example Usage

a=(1,2,3), b=(4,5,6): i=(2·6-3·5)=12-15=-3, j=-(1·6-3·4)=-(6-12)=6, k=(1·5-2·4)=5-8=-3. a×b = (-3, 6, -3).

Recall Trigger

'I Just Kidding' — i(+), j(-), k(+) for cross product expansion.

Topic

Vectors

Concept

Dot product is SCALAR; Cross product is VECTOR

Anchor Id

A15

Difficulty

easy

Memory Aid

Short board exam rhyme: 'DOT gives a NUMBER, plain and simple — CROSS gives a VECTOR, with direction to ripple!' OR use the shape: DOT (·) is a POINT — points have no direction, just a value (scalar). CROSS (×) is an X with TWO arms pointing outward — that X shape shows it goes somewhere in space (vector). 'Dot = dot on number line = scalar. Cross = X marks a direction in space = vector.'

Anchor Type

rhyme

Why It Works

The rhyme provides phonetic encoding. The visual shape comparison (· is a point = scalar; × has direction = vector) adds a second encoding channel, doubling retention.

Example Usage

Board question: 'Which operation yields a scalar?' — immediately recall: DOT product = scalar. 'Which yields a vector?' — CROSS product = vector.

Recall Trigger

Dot (·) = point = scalar. Cross (×) = X with direction = vector.

Topic

Complex Numbers

Concept

Exponential form of complex number: z = re^(iθ)

Anchor Id

A16

Difficulty

hard

Memory Aid

Euler's formula links e^(iθ) = cosθ + i·sinθ. Think of it as the SWISS ARMY KNIFE of complex numbers: one compact form (e^(iθ)) that unfolds into cosine and sine simultaneously. The 'e' stands for 'everything' — it contains both the oscillation (cos) and the perpendicular oscillation (sin) in one symbol. When you see re^(iθ), think: r is the SIZE of the knife, and e^(iθ) is all the TOOLS folded inside (cos and sin).

Anchor Type

analogy

Why It Works

The Swiss army knife analogy communicates compactness and the idea that e^(iθ) encodes two pieces of information (cos and sin) in one symbol, making Euler's formula intuitive.

Example Usage

Convert 5e^(i·53.13°) to rectangular: 5(cos53.13° + i·sin53.13°) = 5(0.6 + 0.8i) = 3 + 4i.

Recall Trigger

Swiss army knife: e^(iθ) unfolds into cosθ + i·sinθ. r is the size.

Topic

Cramer's Rule

Concept

No unique solution when det(A) = 0 (Cramer's Rule fails)

Anchor Id

A17

Difficulty

medium

Memory Aid

Imagine you have a Jollibee coupon (the solution) and you need to redeem it by dividing its value by the store's exchange rate (det A). But if the exchange rate is ZERO, you are dividing by zero — you get UNDEFINED. The coupon system breaks down: no unique meal (no unique solution). This is called a SINGULAR matrix. Board exam alert: whenever you compute det(A) = 0, immediately write 'no unique solution — Cramer's Rule does not apply' and check if the system is inconsistent or has infinitely many solutions.

Anchor Type

micro_story

Why It Works

The Jollibee coupon story creates a relatable scenario. The 'division by zero = system breakdown' connection is mathematically accurate and emotionally memorable through a familiar fast-food brand.

Example Usage

System: x+2y=3, 2x+4y=6. det A = (1)(4)-(2)(2) = 0. Cramer's Rule fails. The system is dependent (infinitely many solutions).

Recall Trigger

det(A) = 0 → dividing by zero → Jollibee coupon fails → no unique solution.

Topic

Vectors

Concept

Finding angle between two vectors using dot product: cosθ = (a·b)/(|a||b|)

Anchor Id

A18

Difficulty

medium

Memory Aid

Remember the formula as 'DOT over MAG-MAG': cosθ = DOT / (MAG of a × MAG of b). The phrase 'Dot over Mag-Mag' has a rhythm to it — say it fast: 'dot-over-mag-mag.' Steps: (1) Compute the dot product (dot), (2) Find |a| and |b| (mag-mag), (3) Divide and take arccos. Procedure: D-M-A: Dot, Mags, Arccos.

Anchor Type

mnemonic

Why It Works

The rhythmic phrase 'dot-over-mag-mag' encodes the structure of the formula. The DMA acronym (Dot, Mags, Arccos) gives the three-step procedure for board exam execution.

Example Usage

a=(1,2,2), b=(2,0,1). Dot = 1·2+2·0+2·1 = 4. |a|=3, |b|=sqrt(5). cosθ = 4/(3·sqrt(5)) = 4/6.708 = 0.5963. θ = arccos(0.5963) ≈ 53.4°.

Recall Trigger

DMA: Dot, Mags, Arccos. cosθ = dot / (mag × mag).

Topic

Complex Numbers

Concept

Polar form: z = r(cosθ + i·sinθ) — also called 'cis' form

Anchor Id

A19

Difficulty

easy

Memory Aid

'CIS' = Cosine + I·Sine. Remember: 'CIS is what r gets multiplied by in polar form.' r·cis(θ) = r(cosθ + i·sinθ). In the Philippines, think of 'CIS' as 'Civil In Structure' — both cosine and sine are structural components (like columns and beams) that together form the polar representation. Some textbooks write r·cis(θ) directly — recognize it instantly as the polar form.

Anchor Type

acronym

Why It Works

The cis notation is commonly seen in Philippine engineering boards. The acronym CIS = Cosine + I·Sine directly decodes the notation, and the civil engineering analogy makes it subject-relevant.

Example Usage

Board question: 'Express 4·cis(60°) in rectangular form.' Recognize as 4(cos60° + i·sin60°) = 4(0.5 + i·0.866) = 2 + 3.464i.

Recall Trigger

CIS = Cosine + I·Sine. r·cis(θ) = r(cosθ + i·sinθ).

Topic

Matrices and Determinants

Concept

Matrix equation Ax = b vs. x = A⁻¹b — order matters in matrix algebra

Anchor Id

A20

Difficulty

hard

Memory Aid

Think of solving Ax = b like solving for x in arithmetic: if 3x = 6, you divide both sides by 3, which means multiplying by (1/3) = 3⁻¹ on the LEFT. Same with matrices: x = A⁻¹b. The A⁻¹ must go on the LEFT of b because matrices are not commutative — if you write bA⁻¹, you are saying 'multiply b from the right' which is a different operation and gives wrong dimensions. The mnemonic: 'Inverse is always the FIRST to act on b — LEFT is right for the inverse!' Never write x = bA⁻¹.

Anchor Type

micro_story

Why It Works

The arithmetic analogy (3x = 6 → x = (1/3)·6) builds on a simpler, already-known operation to justify the matrix procedure. The memorable phrase 'LEFT is right for the inverse' is paradoxically structured for stickiness.

Example Usage

Solve Ax=b where A=[[2,1],[5,3]], b=[4,7]. Find A⁻¹: det=1, A⁻¹=[[3,-1],[-5,2]]. x = A⁻¹b = [[3,-1],[-5,2]]·[4,7] = [12-7, -20+14] = [5, -6].

Recall Trigger

'LEFT is right!' — A⁻¹ always goes on the LEFT of b when solving Ax=b.

Revision Game

Magnitude |z| = sqrt(25 + 144) = sqrt(169) = 13

Clue

I am the Pythagorean theorem in disguise. Given z = 5 + 12i, what is my value?

Memory Link

A2 — Binondo diagonal shortcut analogy. The 5-12-13 is a Pythagorean triple.

det(A) — the determinant of the coefficient matrix

Clue

I am the 'master key' in Cramer's Rule. If I equal zero, the hotel is closed. What am I?

Memory Link

A10 and A17 — Master key / Jollibee coupon story. det(A) = 0 means no unique solution.

A⁻¹ — the inverse matrix, computed by Swap, Negate, Divide

Clue

I follow the rule of SND. I am the matrix that undoes what A does. What am I?

Memory Link

A9 — SND mnemonic for 2×2 matrix inverse.

r^6 = 1^6 = 1, angle = 6 × 30° = 180°. Answer: 1∠180° = -1 + 0i = -1

Clue

Raise the radius, spin the angle — that is De Moivre's game. Compute (1∠30°)^6.

Memory Link

A4 — De Moivre rhyme: Raise the r, spin the θ.

The dot product (a·b = |a||b|cosθ = 0 when θ = 90°)

Clue

I am a scalar. I equal zero when two vectors are perpendicular. What operation am I?

Memory Link

A12 and A15 — Dot product agreement meter; dot = point = scalar.

The cross product a × b

Clue

I am a vector perpendicular to both a and b. My magnitude equals the area of their parallelogram. What am I?

Memory Link

A13 — Right-hand rule and parallelogram area analogy.

Multiply magnitudes: 3×2 = 6. Add angles: 40°+50° = 90°. Answer: 6∠90°

Clue

When multiplying two complex numbers in polar form — (3∠40°)(2∠50°) — what are the two operations you perform?

Memory Link

A6 — Jeepney multiplication: TIMES the distance, PLUS the direction.

Columns — Cramer Changes Columns (replace the i-th column with vector b, never a row)

Clue

I am CCC — I remind you that Cramer only does this to the matrix, never to rows. What do I change?

Memory Link

A11 — CCC mnemonic: Cramer Changes Columns.

e = Euler's number (≈2.718), i = imaginary unit, θ = angle in radians, cosθ = real part, sinθ = imaginary part coefficient.

Compute det(A) = ad - bc
Check det(A) ≠ 0
Swap a and d (main diagonal elements)
Negate b and c (off-diagonal elements)
Multiply entire matrix by 1/det(A)

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GELE Mathematics — Advanced Engineering MathematicsMemory Anchors

Exam context

Advanced Engineering Mathematics - Memory Anchors

Anchors

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