First slide

Operations of matrix

Question

Let $A = (\begin{array}{ll} 4 3 \\ 2 5 \end{array})$ and $x, y \in R$ are such that $A^{2} + x A + y I = 0$ then (x,y) equals

Easy

A

$(- 9, - 14)$
B

$(9, - 14)$
C

$(- 9, 14)$
D

$(9, 14)$

Solution

We have $A^{2} = (\begin{array}{ll} 22 27 \\ 18 31 \end{array})$
$∴ A^{2} + x A + y I = O$
$\begin{array}{l} \Rightarrow 22 + 4 x + y = 0, 27 + 3 x = 0 \\ 18 + 2 x = 0, 31 + 5 x + y = 0 \\ \Rightarrow x = - 9, y = 14 \end{array}$

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