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If A = {bmatrix}1 & 2 & 3 -1 & 1 & 2 2 & 2 & 4{bmatrix} then (

Question

If $A = ⎣ ⎡ 1 - 1 2 212324 ⎦ ⎤$ then $(A^{2} - 5 A) A^{- 1} =$

⎣ ⎡ 4 - 1 1 242321 ⎦ ⎤

⎣ ⎡ - 4 - 1 2 2 - 4 2 32 - 1 ⎦ ⎤

⎣ ⎡ - 4 23 - 1 - 4 2 12 - 1 ⎦ ⎤

⎣ ⎡ - 1 41 - 2 - 2 4 1 - 3 - 2 ⎦ ⎤

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A = ⎣ ⎡ 1 - 1 2 212324 ⎦ ⎤

then

(A^{2} - 5 A) A^{- 1} =

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Text solutionVerified

A = ⎣ ⎡ 1 - 1 2 212324 ⎦ ⎤

⎣ ⎡ 1 - 1 2 212324 ⎦ ⎤

To find

(A^{2} - 5 A) A^{- 1}

(A^{2} - 5 A) A^{- 1} = A^{2} \cdot A^{- 1} - 5 A A^{- 1}

= A \cdot A A^{- 1} - 5 I

= A - 5 I

(A^{2} - 5 A) A^{- 1} = ⎣ ⎡ 1 - 1 2 212324 ⎦ ⎤ - 5 ⎣ ⎡ 100010001 ⎦ ⎤

(A^{2} - 5 A) A^{- 1} = ⎣ ⎡ - 4 - 1 2 2 - 4 2 32 - 1 ⎦ ⎤

∴ (A^{2} - 5 A) A^{- 1} = ⎣ ⎡ - 4 - 1 2 2 - 4 2 32 - 1 ⎦ ⎤

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