(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,which

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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,which is equal to $|A|$.$|A| = \begin{vmatrix} 3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6 \end{vmatrix}$Expanding along the first row:$|A| = 3(2 \times 6 - 1 \times 2) - 2(1 \times 6 - 1 \times 3) + 4(1 \times 2 - 2 \times 3)$$|A| = 3(12 - 2) - 2(6 - 3) + 4(2 - 6)$$|A| = 3(10) - 2(3) + 4(-4)$$|A| = 30 - 6 - 16$$|A| = 8$Therefore,$a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13} = 8$.

Class 12 Mathematics 3-4. Matrices and Determinants Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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

MHT CET 2021 All MHT CET

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

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Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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

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