(B) Given the matrix $A = \begin{bmatrix} 5x & 10 \\ 8 & 7 \end{bmatrix}$.The determinant of a $2 \times 2$ matrix $\begin{bmatrix} a & b \\ c & d \en

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(B) Given the matrix $A = \begin{bmatrix} 5x & 10 \\ 8 & 7 \end{bmatrix}$.The determinant of a $2 \times 2$ matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is calculated as $|A| = ad - bc$.Applying this to matrix $A$:$|A| = (5x)(7) - (10)(8)$$|A| = 35x - 80$We are given that $|A| = 25$. Therefore:$35x - 80 = 25$$35x = 25 + 80$$35x = 105$$x = \frac{105}{35}$$x = 3$Thus,the correct value is $3$.

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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If $A = \begin{bmatrix} 5x & 10 \\ 8 & 7 \end{bmatrix}$ and $|A| = 25$,then $x = $ . . . . . . .

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A
$3$ and $-3$
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$3$
C
$-3$
D
$3$ or $-3$

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3 and 4 .Determinants and Matrices

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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 $A = \begin{bmatrix} 5x & 10 \\ 8 & 7 \end{bmatrix}$ and $|A| = 25$,then $x = $ . . . . . . .

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