If A - begin bmatrix 381 1-1 - 2lendbmatrix - show that A 2-5 A - I -0-

Given, A =[ 3 amp; 1; 1 amp; 2 ] Now, A^2 =AA=[ 3 amp; 1; 1 amp; 2; ][ 3 amp; 1; 1 amp; 2; ]=[ 9 1 amp; 3+2 ...

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Inverse of a Matrix

If A = begin ...

Question

If $A = [\begin{matrix} 3 & 1 - 1 & 2 \end{matrix}]$ , show that $A^{2} - 5 A + I = 0.$

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If $A = [\begin{matrix} 3 & 1 - 1 & 2 \end{matrix}]$ , show that $A^{2} - 5 A + 7 I = 0$ . Hence, find $A^{- 1}$

A = [\begin{matrix} 3 & 1 - 1 & 2 \end{matrix}]

I = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]

A^{2} = 5 A + k I

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & - 1 2 & 1 & - 1 2 & 3 & 2 \end{matrix} ⎤ ⎥ ⎦

A^{- 1}

B

A^{2} + A + I = B A

A = [\begin{matrix} 3 & 1 - 1 & 2 \end{matrix}]

I = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]

A^{2} - 5 A + 7 I

A = [\begin{matrix} 3 & 1 - 1 & 2 \end{matrix}],

A^{2} - 5 A + 7 I = 0.

A^{4}

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