question_answer

For what value of k, the matrix \[\left[ \begin{matrix}    2-k & 4  \\    -\,5 & 1  \\ \end{matrix} \right]\] is not invertible?     

Answer:

Given matrix\[A=\left[ \begin{matrix}    2-k & 4  \\    -\,5 & 1  \\ \end{matrix} \right]\]is not invertible. i.e. A is singular matrix, then \[|A|\,\,=0\]. \[\Rightarrow \]               \[\left| \begin{matrix}    2-k & 4  \\    -\,5 & 1  \\ \end{matrix} \right|=0\] \[\Rightarrow \]               \[2-k+20=0\] \[\Rightarrow \]               \[22-k=0\]          \[\therefore \]                  \[k=22\]