For the matrix A=3211, the values of a and b such that A2 + aA + bI = O are.

A2 + aA + bI = O11843+3a2aaa+b00b=O3a+b+11=0, 2a+8=0∴b-1=0 a=-4b=1

For the matrix A=3211, the values of a and b such that A2 + aA + bI = O are.

A2 + aA + bI = O11843+3a2aaa+b00b=O3a+b+11=0, 2a+8=0∴b-1=0 a=-4b=1

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For the matrix $A = [\begin{matrix} 3 & 2 \\ 1 & 1 \end{matrix}],$ the values of a and b such that $A^{2} + aA + bI = O$ are.

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–4, 1

–2, 3

1, 4

2, 3

answer is C.

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Detailed Solution

$A^{2} + aA + bI = O$

$\begin{array}{rcl} [\begin{matrix} 11 & 8 \\ 4 & 3 \end{matrix}] + [\begin{matrix} 3 a & 2 a \\ a & a \end{matrix}] + [\begin{matrix} b & 0 \\ 0 & b \end{matrix}] & = & O \\ 3 a + b + 11 & = & 0, 2 a + 8 = 0 \\ ∴ b - 1 & = & 0 a = - 4 \\ b & = & 1 \end{array}$