Technique

Row and column operations

R_i \to R_i + \lambda R_j \;\Rightarrow\; \det A \text{ unchanged}

$R_i, C_i$: the i-th row and column

Adding a multiple of one row or column to another leaves the determinant unchanged, which is what makes a determinant collapsible before expansion.

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#1NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#2NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#3NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
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#4NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#5NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#6NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#7NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
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#8NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#9NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#10NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#11NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#12NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#13NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#14NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#15NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#16NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#17NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#18NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#19NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#20NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#21NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#22NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#23NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#24NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#25NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#26NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#27NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
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#28NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#29NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#31NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#32NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#33NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#34NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#35NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#36NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#37NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#38NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#39NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#40NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#41NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#42CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#43CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#44NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#45NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#46NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#47NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#48NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#49NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#50NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#51NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#52NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#53NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#54NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#55NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#56NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#57NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#58NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#61NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#65NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#66NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#67NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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