(A) To find the determinant of matrix $A$, we expand along the first row: $\operatorname{det}(A) = 2 \begin{vmatrix} 7 & 11 \\ 4 & 8 \end{vmatrix} - 0

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$\operatorname{det} A$ is divisible by $11$

(A) To find the determinant of matrix $A$, we expand along the first row: $\operatorname{det}(A) = 2 \begin{vmatrix} 7 & 11 \\ 4 & 8 \end{vmatrix} - 0 \begin{vmatrix} 4 & 11 \\ 5 & 8 \end{vmatrix} + 3 \begin{vmatrix} 4 & 7 \\ 5 & 4 \end{vmatrix}$ $= 2(56 - 44) - 0 + 3(16 - 35)$ $= 2(12) + 3(-19)$ $= 24 - 57$ $= -33$ Since $-33 = 11 \times (-3)$, the value of $\operatorname{det} A$ is divisible by $11$.

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

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Let $A = \begin{bmatrix} 2 & 0 & 3 \\ 4 & 7 & 11 \\ 5 & 4 & 8 \end{bmatrix}$. Then

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A
$\operatorname{det} A$ is divisible by $11$
B
$\operatorname{det} A$ is not divisible by $11$
C
$\operatorname{det} A = 0$
D
$A$ is an orthogonal matrix

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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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