Paragraph: Let Δ be the determinant of a matrix A , where A= ( array lll a_ 11 & a_ 12 & a_ 13 a_ 21 & a_ 22 & a_ 23 a_ 31 & a_ 32 & a_ 33 array ) and C_ 11 , C_ 12 , C_ 13 be the cofactors of a_ 11 , a_ 12 , a_ 13

Correct answer: A. 0 We know that a_ 21 C_ 11 +a_ 22 C_ 12 +a_ 23 C_ 13 =O

NDA 2022

Exam: NDA
Year: 2022
Subject: Mathematics
Chapter: Determinants

NDA 2022 · Mathematics · Determinants

Paragraph: Let Δ be the determinant of a matrix A , where A= (...

Paragraph: Let

\Delta

be the determinant of a matrix

A

, where

A=

\left(

\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}

\right)

and

C_{11}, C_{12}, C_{13}

be the cofactors of

a_{11}, a_{12}, a_{13}

respectively.<br><strong>Question:</strong> What is the value of

a_{21} C_{11}+a_{22} C_{12}+a_{23} C_{13} ?

Options

A $0$
B $1$
C $\Delta$
D $-\Delta$

Correct answer

A. $0$

Step-by-step solution

We know that

a_{21} C_{11}+a_{22} C_{12}+a_{23} C_{13}=\mathrm{O}

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