(A) The expression $a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13}$ represents the expansion of the determinant of matrix $A$ along the first row.There

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(A) The expression $a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13}$ represents the expansion of the determinant of matrix $A$ along the first row.Therefore,$a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13} = |A|$.$|A| = 3 \begin{vmatrix} 2 & 1 \\ 2 & 6 \end{vmatrix} - 2 \begin{vmatrix} 1 & 1 \\ 3 & 6 \end{vmatrix} + 4 \begin{vmatrix} 1 & 2 \\ 3 & 2 \end{vmatrix}$.$|A| = 3(12 - 2) - 2(6 - 3) + 4(2 - 6)$.$|A| = 3(10) - 2(3) + 4(-4)$.$|A| = 30 - 6 - 16 = 8$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Minors and Co-factors, Product of determinants

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If $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6 \end{bmatrix}$ and $A_{ij}$ are the cofactors of $a_{ij}$,then $a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13}$ is equal to

MHT CET 2009 All MHT CET

A
$8$
B
$6$
C
$4$
D
$0$

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3 and 4 .Determinants and Matrices

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Minors and Co-factors, Product of determinants

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If $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6 \end{bmatrix}$ and $A_{ij}$ are the cofactors of $a_{ij}$,then $a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13}$ is equal to

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Write the minors and cofactors of the elements of the following determinant: $\left|\begin{array}{ccc}1 & 0 & 4 \\ 3 & 5 & -1 \\ 0 & 1 & 2\end{array}\right|$

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