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प्रश्न
Given A = `[(2, 2, -4),(-4, 2, -4),(2, -1, 5)]`, B = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)]`, find BA and use this to solve the system of equations y + 2z = 7, x – y = 3, 2x + 3y + 4z = 17.
उत्तर
We have, A = `[(2, 2, -4),(-4, 2, -4),(2, -1, 5)]` and B = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)]`
∴ BA = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)] [(2, 2, -4),(-4, 2, -4),(2, -1, 5)]`
= `[(6, 0, 0),(0, 6, 0),(0, 0, 6)]`
= 6I
∴ B–1 = `"A"/6 = 1/6 [(2, 2, -4),(-4, 2, -4),(2, -1, 5)]` ....(i)
Given system of equation is:
x – y = 3
2x + 3y + 4z = 17
And y + 2z = 7
or `[(1, -1, 0),(2, 3, 4),(0, 1, 2)] [(x),(y),(z)] = [(3),(17),(7)]`
∴ `[(x),(y),(z)] = [(1, -1, 0),(2, 3, 4),(0, 1, 2)]^-1 [(3),(17),(7)]`
= `1/6 [(2, 2, -4),(-4, 2, -4),(2, -1, 5)] [(3),(17),(7)]`
= `1/16 [(6 + 34 - 28),(-12 + 34 - 28),(6 - 17 + 35)]`
= `1/6 [(12),(-6),(24)]`
= `[(2),(-1),(4)]`
∴ x = 2, y = –1 and z = 4
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