If A = [ 3 1 - 1 2 ] , then A 2 - 5 A + 7 I =

Question

If $A = [\begin{matrix} 3 & 1 \\ - 1 & 2 \end{matrix}],$ then $A^{2} - 5 A + 7 I =$

Smart Achievers · Accepted Answer

(1)

Ans. 0

Explanation:

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

$A^{2} - 5 A + 7 I = ?$

$A^{2} = [\begin{matrix} 3 & 1 \\ - 1 & 2 \end{matrix}] [\begin{matrix} 3 & 1 \\ - 1 & 2 \end{matrix}] = [\begin{matrix} 8 & 5 \\ - 5 & 3 \end{matrix}]$

$- 5 A = - 5 [\begin{matrix} 3 & 1 \\ - 1 & 2 \end{matrix}] = [\begin{matrix} - 15 & - 5 \\ 5 & - 10 \end{matrix}]$

$7 I = 7 [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = [\begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}]$

$A^{2} - 5 A + 7 I = [\begin{matrix} 8 & 5 \\ - 5 & 3 \end{matrix}] + [\begin{matrix} - 15 & - 5 \\ 5 & - 10 \end{matrix}] + [\begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}]$

$= [\begin{matrix} 8 - 15 + 7 & 5 - 5 + 0 \\ - 5 + 5 + 0 & 3 - 10 + 7 \end{matrix}] = 0$

Solution

Q.
If $A = [\begin{matrix} 3 & 1 \\ - 1 & 2 \end{matrix}],$ then $A^{2} - 5 A + 7 I =$

1 $0$

2 $I$

3 $2 I$

4 $3 I$

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Solution

Q. If A=[31-12], then A2-5A+7I=

1 0

2 I

3 2I

4 3I