Let A= [ 5 5 α α 0 α 5 α 0 0 5 ] . If |A^2 |=25 , then |α| equals

Correct answer: (C) 1 / 5. A^2= [ 5 5 α α 0 α 5 α 0 0 5 ] [ 5 5 α α 0 α 5 α 0 0 5 ] A^2= [ 25 25 α+5 α^2 5 α+25 α^2+5 α 0 α^2 5 α^2+25 α 0 0 25 ] 625 α^2=25 ⇒|α|=1/5 .

Q62 / 120 · JEE Main 2007 · Mathematics

Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$. If $\left|A^2\right|=25$, then $|\alpha|$ equals

A
$5^2$
B
$1$
Correct answer
C
$1 / 5$
D
$5$

Solution

$\mathrm{A}^2=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$ $\mathrm{A}^2=\left[\begin{array}{ccc}25 & 25 \alpha+5 \alpha^2 & 5 \alpha+25 \alpha^2+5 \alpha \\ 0 & \alpha^2 & 5 \alpha^2+25 \alpha \\ 0 & 0 & 25\end{array}\right]$ $625 \alpha^2=25$ $\Rightarrow|\alpha|=\frac{1}{5}$.

Hence, the correct answer is option: 'C'.

Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$. If $\left|A^2\right|=25$, then $|\alpha|$ equals

Solution

Relevant Questions