If $B = \begin{bmatrix} 5 & 2\alpha & 1 \ 0 & 2 & 1 \ \alpha & 3 & -1 \end{bmatrix}$ is the inverse of a $3 imes 3$ matrix $A$, then the sum of all values of $\alpha$ for which $\det(A) + 1 = 0$, is:

Question

If $B = \begin{bmatrix} 5 & 2\alpha & 1 \ 0 & 2 & 1 \ \alpha & 3 & -1 \end{bmatrix}$ is the inverse of a $3 	imes 3$ matrix $A$, then the sum of all values of $\alpha$ for which $\det(A) + 1 = 0$, is:

Aicharya · Accepted Answer

Since, A = - 1 Hence, B = 1 | A | = - 1 &#8658; B = 5 - 5 - 2 &#945; - &#945; - 2 &#945; = 2 &#945; 2 - 2 &#945; - 25 1 + A = 0 &#945; 2 - &#945; - 12 = 0 Sum = 1

If $B = \begin{bmatrix} 5 & 2\alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1 \end{bmatrix}$ is the inverse of a…

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