First slide

Operations of matrix

Question

Let $A = [\begin{array}{ll} 3 2 \\ 1 1 \end{array}]$ satisfies $A^{2} + a A + b I = O$ , then a, b are respectively equal to

Easy

A

– 4, 2
B

–3, 3
C

– 4, 1
D

–3, 1

Solution

$A^{2} = [\begin{array}{ll} 3 2 \\ 1 1 \end{array}] [\begin{array}{ll} 3 2 \\ 1 1 \end{array}] = [\begin{array}{ll} 11 8 \\ 4 3 \end{array}]$
Now $O = A^{2} + a A + b I = [\begin{array}{cc} 11 + 3 a + b & 8 + 2 a \\ 4 + a & 3 + a + b \end{array}]$
$\begin{array}{l} \Rightarrow 3 a + b = - 11, 4 + a = 0, a + b = - 3 \\ \Rightarrow a = - 4, b = 1 . \end{array}$

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