Question

If A² = 8A + kI where A = $\begin{bmatrix} 1 & 0 \

• 1 & 7 \end{bmatrix}$ then k is :

• A. 7
• B. –7
• C. 1
• D. –1

Answer 1

Answer: (B)

–7

Answer 2

$\left[ \begin{array} { c c } 1 , & 0 \\ - 1 , & 7 \end{array} \right]$ $\left[ \begin{array} { c c } 1 , & 0 \\ - 1 , & 7 \end{array} \right]$ = 8$\begin{bmatrix} 1, & 0 \

• 1, & 7 \end{bmatrix}$+ k$\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$

or $\begin{bmatrix} 1 + 0 & 0 + 0 \

• 1 - 7 & 0 + 49 \end{bmatrix}$= z$\begin{bmatrix} 8 & 0 \
• 8 & 56 \end{bmatrix}$+$\begin{bmatrix} k & 0 \ 0 & k \end{bmatrix}$

or $\begin{bmatrix} 1 & 0 \

• 8 & 49 \end{bmatrix}$=$\begin{bmatrix} k + 8 & 0 \
• 8 & k + 56 \end{bmatrix}$

̃1 = k + 8

49 = k + 56

̃k = – 7