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Question
If A = `[(1,0,1),(0,2,3),(1,2,1)]` and B = `[(1,2,3),(1,1,5),(2,4,7)]`, then find a matrix X such that XA = B.
Solution
Consider XA = B
∴ X `[(1,0,1),(0,2,3),(1,2,1)] = [(1,2,3),(1,1,5),(2,4,7)]`
By C3 - C1 we get,
X `[(1,0,1),(0,2,3),(1,2,0)] = [(1,2,2),(1,1,4),(2,4,7)]`
By `(1/2)"C"_2` we get,
X `[(1,0,0),(0,1,3),(1,1,0)] = [(1,1,2),(1,1/2,4),(2,2,5)]`
By C3 - 3C2 we get,
X `[(1,0,0),(0,1,0),(1,1,-3)] = [(1,1,-1),(1,1/2,5/2),(2,2,-1)]`
By `(-1/3)` C3, we get
X `[(1,0,0),(0,1,0),(1,1,1)] = [(1,1,1/3),(1,1/2,-5/6),(2,2,1/3)]`
By C1 - C3 and C2 - C3 we get,
X `[(1,0,0),(0,1,0),(0,0,1)] = [(2/3,2/3,1/3),(11/6,4/3,-5/6),(5/3,5/3,1/3)]`
∴ X = `1/6 [(4,4,2),(11,8,-5),(10,10,2)]`
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