Search any question & find its solution
Question:
Answered & Verified by Expert
If the matrix $\left[\begin{array}{ccc}\alpha & 2 & 2 \\ -3 & 0 & 4 \\ 1 & -1 & 1\end{array}\right]$ is not invertible, then:
Options:
Solution:
1415 Upvotes
Verified Answer
The correct answer is:
$\alpha=-5$
Let $\mathrm{A}=\left[\begin{array}{ccc}\alpha & 2 & 2 \\ -3 & 0 & 4 \\ 1 & -1 & 1\end{array}\right]$
$|\mathrm{A}|=\left|\begin{array}{ccc}\alpha & 2 & 2 \\ -3 & 0 & 4 \\ 1 & -1 & 1\end{array}\right|$
$|A|=\alpha(0+4)-2(-3-4)+2(3-0)=4 \alpha+20$
Since $\mathrm{A}^{-1}$ does not exist, $\therefore|\mathrm{A}|=0$
$4 \alpha+20=0$
$4 \alpha=-20$
$\alpha=-5$
$|\mathrm{A}|=\left|\begin{array}{ccc}\alpha & 2 & 2 \\ -3 & 0 & 4 \\ 1 & -1 & 1\end{array}\right|$
$|A|=\alpha(0+4)-2(-3-4)+2(3-0)=4 \alpha+20$
Since $\mathrm{A}^{-1}$ does not exist, $\therefore|\mathrm{A}|=0$
$4 \alpha+20=0$
$4 \alpha=-20$
$\alpha=-5$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.