Question

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

• A. 4
• B. 5
• C. 6
• D. 7
• E. 8

Answer 1

Answer: (E)

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