Question

If A = $\left[\begin{array}{ccc}2&4\\-1&k\end{array}\right]$ and A2 = O, then find the value of k.

Answer 1

Answer:

k= ± 2

Step-by-step explanation:

If

$A=\left[\begin{array}{ccc}2&4\\-1&k\end{array}\right]$  and

A² = O, then find the value of k.

So,find

$A^{2}=A\times A=\left[\begin{array}{ccc}2&4\\-1&k\end{array}\right]\times \left[\begin{array}{ccc}2&4\\-1&k\end{array}\right]$

$A^{2}=\left[\begin{array}{ccc}0&4k+8\\-(k+2)&k^{2}-4\end{array}\right]$

according to the given condition

$A^{2}=\left[\begin{array}{ccc}0&4k+8\\-(k+2)&k^{2}-4\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]$

4k-8=0

4k=8

k=2

or k²=4

k=±2