Question

If $A=\left[\begin{array}{ccc}2& 0& 1\\ 2& 1& 3\\ 1& -1& 0\end{array}\right]$, then $A^2-5A+6I=$

• A. $\left[\begin{array}{ccc}1& -1& 5\\ -1& -1& 4\\ -3& -10& 4\end{array}\right]$
• B. $\left[\begin{array}{ccc}1& -1& -3\\ -1& -1& -10\\ -5& 4& 4\end{array}\right]$
• C. $3$
• D. $I$

Answer 1

Answer: (B)

$\left[\begin{array}{ccc}1& -1& -3\\ -1& -1& -10\\ -5& 4& 4\end{array}\right]$

$A^2=\left[\begin{array}{ccc}2& 0& 1\\ 2& 1& 3\\ 1& -1& 0\end{array}\right]\left[\begin{array}{ccc}2& 0& 1\\ 2& 1& 3\\ 1& -1& 0\end{array}\right]=\left[\begin{array}{ccc}5& -1& 2\\ 9& -2& 5\\ 0& -1& -2\end{array}\right]$
$A^2-5A+9I=\left[\begin{array}{ccc}5-10+6& -1+0+0& 2-5+0\\ 9-10+0& -2-5+6& 5-15+0\\ 0-5+0& -1+5+0& -2+0+6\end{array}\right]=\left[\begin{array}{ccc}1& -1& -3\\ -1& -1& -10\\ -5& 4& 4\end{array}\right]$
Ans: B