The value of the determinant $\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}$ is:

Question

Let
\[ f(x)=\int \frac{7x^{10}+9x^8}{(1+x^2+2x^9)^2}\,dx,\quad x > 0, \] and
\[ A= \begin{bmatrix} 0 & 0 & 1 \\ \frac{1}{4} & f'(1) & 1 \\ \alpha & 4 & 1 \end{bmatrix}. \] If $ B=\operatorname{adj}(\operatorname{adj} A) $, then the value of $ \alpha $ for which $ \det(B)=1 $ is

Answer 1

To find the value of the determinant of a 2x2 matrix, we use the formula:

$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc$

For the given matrix, we have:

1	2
3	4

Identify the elements $a = 1$, $b = 2$, $c = 3$, and $d = 4$.
Substitute these into the determinant formula: $ad - bc$.
Calculate: $1 \times 4 - 2 \times 3 = 4 - 6 = -2$.

Therefore, the value of the determinant is $-2$.

This matches the given correct answer.

The value of the determinant $\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}$ is:

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The Correct Option is B

Solution and Explanation

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