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Question
Find X, if AX = B, where A = `[(1,2,3),(-1,1,2),(1,2,4)]` and B = `[(1),(2),(3)]`
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Solution
AX = B
∴ `[(1,2,3),(-1,1,2),(1,2,4)] "X" = [(1),(2),(3)]`
By R2 + R1 and R3 - R1, we get,
`[(1,2,3),(0,3,5),(0,0,1)] "X"= [(1),(3),(2)]`
By `(1/3)"R"_2,` we get,
`[(1,2,3),(0,1,5/3),(0,0,1)] "X" = [(1),(1),(2)]`
By R1 - 2R2, we get,
`[(1,0,-1/3),(0,1,5/3),(0,0,1)] "X" = [(-1),(1),(2)]`
By `"R"_1 + 1/3"R"_3 "and" "R"_2 - 5/3 "R"_3` we get,
`[(1,0,0),(0,1,0),(0,0,1)] "X" = [(-1/3),(-7/3),(2)]`
`∴ "X" = [(-1/3),(-7/3),(2)]`
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