If A - - 1 -1- 2 3 - then show that A2 - 4A - 5I2 - 0

We can write A^2 = AA = [ #160;1 amp; 1; 2 #160; amp; 3 ][ #160;1 amp; 1; 2 #160; amp; 3 ] = [ #160;1 2 amp; 1 3; 2 ...

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Multiplication of Matrices

If A = [ 1 ...

Question

If $A = (\begin{matrix} 1 & - 1 2 & 3 \end{matrix})$ , then show that $A^{2} - 4 A + 5 I_{2} = 0$

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Solution

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

A^{2} - 4 A + 5 I_{2} = O

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

A^{2} - 4 A + 5 I = 0

I

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

I

2

A^{2} - 4 A + 5

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

A^{2} - 4 A - 5 I = 0.

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

A^{2} - 4 A - 5 I = 0

A^{- 1}

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