Question

A² = 8A+KI
find the matrix of K​

Answer 1

Answer:

    $\left[\begin{array}{ccc}1&0\\-1&7\end{array}\right] ^{2} = 8\left[\begin{array}{ccc}1&0\\-1&7\end{array}\right] + k \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

⇒  $\left[\begin{array}{ccc}1&0\\-8&49\end{array}\right] -\left[\begin{array}{ccc}8&0\\-8&56\end{array}\right] = k\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

⇒$\left[\begin{array}{ccc}-7&0\\0&-7\end{array}\right] = \left[\begin{array}{ccc}k&0\\0&k\end{array}\right]$

∴ k= -7

Step-by-step explanation: