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प्रश्न
If A = `[(1,1),(1,2)], "B" = [(4,1),(3,1)]` and C = `[(24,7),(31,9)]`, then find the matrix X such that AXB = C
उत्तर
Since, AXB = C
∴ `[(1,1),(1,2)] ("XB") = [(24,7),(31,9)]`
First we perform the row transformations.
Applying R2 → R2 − R1,
`[(1,1),(0,1)] ("XB") = [(24,7),(7,2)]`
Applying R2 → R1 − R2,
`[(1,0),(0,1)] ("XB") = [(17,5),(7,2)]`
∴ XB = `[(17,5),(7,2)]`
∴ X `[(4,1),(3,1)] = [(17,5),(7,2)]`
Now, we perform the column transformations.
Applying C1 ↔ C2,
`"X" [(1,4),(1,3)] = [(5,17),(2,7)]`
Applying C2 → C2 − 4C1,
`"X"[(1,0),(1,-1)] = [(5,-3),(2,-1)]`
Applying C2 → −C2,
`"X"[(1,0),(1,1)] = [(5,3),(2,1)]`
Applying C1 → C1 − C2,
`"X"[(1,0),(0,1)] = [(2,3),(1,1)]`
∴ X = `[(2,3),(1,1)]`
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