THETA DIVISION

Question 43

Matrices★★★★Question Bank

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Question

Given that matrix

A=\begin{pmatrix}x&3\\5&-1\end{pmatrix}

and matrix

B=\begin{pmatrix}1&-5\\x^2&2x\end{pmatrix}

, the product

A\cdot B

results in an invertible matrix with a determinant equal to

-42x^2

. Determine the product of all values of

x

that satisfies these conditions.

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