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Question
For what value of x the matrix A is singular?
\[ A = \begin{bmatrix}1 + x & 7 \\ 3 - x & 8\end{bmatrix}\]
Solution
Matrix A will be singular if [ A ] = 0
\[\left| A \right| = \begin{vmatrix}1 + x & 7 \\ 3 - x & 8\end{vmatrix} = 0\]
\[ \Rightarrow 8 + 8x - 21 + 7x = 0\]
\[ \Rightarrow 15x - 13 = 0\]
\[ \Rightarrow 15x = 13\]
\[ \Rightarrow x = \frac{13}{15}\]
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