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प्रश्न
Find the matrix X such that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`
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उत्तर
Given that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`
Applying R2 → R2 – 2R1 and R3 → R3 – R1, we get
`[(1, 2, 3),(0, -1, -4),(0, 0,-1)]` X = `[(2, 2, -5),(-6, -5, 14),(-1, -2, 4)]`
Applying R2 → R2 – 4R3, we get
`[(1, 2, 3),(0, -1, 0),(0, 0,-1)]` X = `[(2, 2, -5),(-2, 3, -2),(-1, -2, 4)]`
Applying R1 → R1 + 2R2, we get
`[(1, 0, 3),(0, -1, 0),(0, 0,-1)]` X = `[(-2, 8, -9),(-2, 3, -2),(-1, -2, 4)]`
Applying R1 → R1 + 3R3, we get
`[(1, 0, 0),(0, -1, 0),(0, 0,-1)]` X = `[(-5, 2, 3),(-2, 3, -2),(-1, -2, 4)]`
Applying R2 → (–1)R2 and R3 → (–1)R3, we get
`[(1, 0, 0),(0, 1, 0),(0, 0,1)]` X = `[(-5, 2, 3),(2, -3, 2),(1, 2, -4)]`
∴ X = `[(-5, 2, 3),(2, -3, 2),(1, 2, -4)]`
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