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Question
Find matrix X, if AX = B, where A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)] "and B" = [(1),(2),(3)]`.
Solution
Given,AX = B
∴ `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)] "X" = [(1),(2),(3)]`
Applying R2 → R2 + R3
`[(1, 2, 3),(0, 3, 6),(1, 2, 4)] "X" = [(1),(5),(3)]`
R3 → R3 – R1, we get
`[(1, 2, 3),(0, 3, 6),(0, 0, 1)] "X" = [(1),(5),(2)]`
R2 →`R_2/3`
`[(1, 2, 3),(0, 1, 2),(0, 0, 1)] "X" = [(1),(5/3),(2)]`
Applying R2 → R2 - 2R3
`[(1, 2, 3),(0, 1, 0),(0, 0, 1)] "X" = [(1),(-7/3),(2)]`
R1 → R1 – 3R3
`[(1, 2, 0),(0, 1, 0),(0, 0, 1)] "X" = [(-5),(-7/3),(2)]`
R1 → R1 – 2R2
`[(1, 0, 0),(0, 1, 0),(0, 0, 1)] "X" = [(-1/3),(-7/3),(2)]`
IX = `[(-1/3),(-7/3),(2)]`
X = `[(-1/3),(-7/3),(2)]`
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