Let A=4 32 5 and x,y∈R are such that A2+xA+yI=0 then (x,y) equals

We have A2=22 2718 31∴ A2+xA+yI=O⇒ 22+4x+y=0, 27+3x=018+2x=0, 31+5x+y=0⇒ x=−9,y=14

Let A=4 32 5 and x,y∈R are such that A2+xA+yI=0 then (x,y) equals

We have A2=22 2718 31∴ A2+xA+yI=O⇒ 22+4x+y=0, 27+3x=018+2x=0, 31+5x+y=0⇒ x=−9,y=14

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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

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$(- 9, 14)$

$(9, - 14)$

$(- 9, - 14)$

$(9, 14)$

answer is C.

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Detailed 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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Let A=4 32 5 and x,y∈R are such that A2+xA+yI=0 then (x,y) equals

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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