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Question
if `A = ((2,3,1),(1,2,2),(-3,1,-1))`, Find `A^(-1)` and hence solve the system of equations 2x + y – 3z = 13, 3x + 2y + z = 4, x + 2y – z = 8
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Solution
We have `A = [(2,3,1),(1,2,2),(-3,1,-1)]`
`". |A| = [(2,3,1),(1,2,2),(-3,1,-1)]`
=2(−2 −2) − 3(−1 + 6) +1(1 + 6)
=−8 − 15 + 7=−16 ≠ 0
So, A is invertible.
Let Cij be the co-factors of the elements aij in A[aij]. Then,
Now, the given system of equations is expressible as
Hence, x = 1, y = 2 and z = −3 is the required solution.
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