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Question
If A = `[(3, -5),(-4, 2)]` find A2 – 5A – 14I
Where I is unit matrix of order 2 x 2
Solution
Given
A = `[(3, -5),(-4, 2)]`
A2 = A x A = `[(3, -5),(-4, 2)][(3, -5),(-4, 2)]`
= `[(9 + 20, -15 - 10),(-12 - 8, 20 + 4)]`
= `[(29, -25),(-20, 24)]`
5A = `5[(3, -5),(-4, 2)]`
= `[(15, -25),(-20, 10)]`
∴ A2 – 5A – 14 I = `[(29, -25),(-20, 24)]`
`-[(15, -25),(-20, 10)] -14[(1, 0),(0, 1)]`
= `[(29, -25),(-20, 24)] - [(15, -20),(-20, 10)] - [(14, 0),(0, 1)]`
= `[(29 - 15 - 14, -25 + 25 - 0),(-20 + 20 + 0, 24 - 10 - 14)]`
= `[(0, 0),(0, 0)]`.
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