Property

Proportional rows make a determinant vanish

R_i = \lambda R_j \;\Rightarrow\; \det A = 0

$\lambda$: any scalar

If two rows or columns are equal, or one is a multiple of another, or the rows are otherwise linearly dependent, the determinant is zero.

questions use it

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years it has appeared

22%

rated HARD

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#1NDA → 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 → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#8NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
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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 → Linear Systems — Consistency, Cramer's Rule, Solution Space
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#15NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#16NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#17NDA → Mathematics → Matrices & Determinants → Linear Systems — Consistency, Cramer's Rule, Solution Space
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#18NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#19NDA → 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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Set · 1 question
** Consider the determinant $f(x) = \left| \begin{matrix} x^{2} - 5x + 3 & 2x - 5 & 3 \\ 3x^{2} + x + 4 & 6x + 1 & 9 \\ 7x^{2} - 6x + 9 & 14x - 6 & 21 \end{matrix} \right|$
- #23NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#24NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#31NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#32CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#33CBSE Class 12 → Mathematics → Determinants → Determinant and its Properties
#34NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#35NDA → Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
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#38NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#40NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#41NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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#45NDA → Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
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