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प्रश्न
If A = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]`, find the product (A + I)(A − I)
उत्तर
A + I = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)] + [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
= `[(1+1, 2+0, 0 + 0),(5 + 0, 4+1, 2+0),(0 +0, 7+0,-3+1)]`
= `[(2, 2, 0),(5, 5, 2),(0, 7, -2)]`
A – I = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)] - [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
= `[(1-1, 2-0, 0 - 0),(5 - 0, 4-1, 2-0),(0-0, 7-0,-3-1)]`
= `[(0, 2, 0),(5, 3, 2),(0, 7, -4)]`
∴ (A + I)(A – I) = `[(2, 2, 0),(5, 5, 2),(0, 7, -2)] [(0, 2, 0),(5, 3, 2),(0, 7, -4)]`
= `[(0 + 10 + 0, 4 + 6 + 0, 0 + 4 - 0),(0 + 25 + 0, 10 + 15 + 14, 0 + 10 - 8),(0 + 35 + 0, 0 + 21 - 14,0 + 14 + 8)]`
= `[(10, 10, 4),(25, 39, 2),(35, 7, 22)]`
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