Question

If $A=\left|\begin{array}{ccc}4& k& k\\ 0& k& k\\ 0& 0& k\end{array}\right|$ and det $(A)=256$, then $|k|$ equals

• A. 4
• B. 5
• C. 6
• D. 7
• E. 8

Answer 1

Answer: (E)

We have
$A=\left[\begin{array}{ccc}4& k& k\\ 0& k& k\\ 0& 0& k\end{array}\right]$
$\therefore |A|=\left|\begin{array}{ccc}4& k& k\\ 0& k& k\\ 0& 0& k\end{array}\right|$
$\Rightarrow 256=4\left(k^2-0\right)$
$\Rightarrow 64=k^2$
$\Rightarrow k=\pm 8$
$\therefore |k|=8$