If A = [a_{ij}]_{3 times 3} = begin{bmatrix} | vedclass

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(B) The expression $a_{21} A_{21} + a_{22} A_{22} + a_{23} A_{23}$ represents the expansion of the determinant of matrix $A$ along the second row.Acco

Vedclass · Accepted Answer

$8$

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(B) The expression $a_{21} A_{21} + a_{22} A_{22} + a_{23} A_{23}$ represents the expansion of the determinant of matrix $A$ along the second row.According to the property of determinants,the sum of the products of elements of any row (or column) with their corresponding cofactors is equal to the determinant of the matrix,denoted as $|A|$.$|A| = 3(4 	imes 3 - 1 	imes 6) - 2(1 	imes 3 - 1 	imes 2) + 4(1 	imes 6 - 4 	imes 2)$$|A| = 3(12 - 6) - 2(3 - 2) + 4(6 - 8)$$|A| = 3(6) - 2(1) + 4(-2)$$|A| = 18 - 2 - 8 = 8$.Therefore,$a_{21} A_{21} + a_{22} A_{22} + a_{23} A_{23} = 8$.

If $A = [a_{ij}]_{3 \times 3} = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 4 & 1 \\ 2 & 6 & 3 \end{bmatrix}$ and $A_{ij}$ is the cofactor of $a_{ij}$,then the value of $a_{21} A_{21} + a_{22} A_{22} + a_{23} A_{23}$ is equal to:

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