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Question
Use product `[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)]` to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3
Solution
Since, A × B = I,
∴ B = A−1 .....(1)
Now, the given system of equations is
x + 3z = 9
−x + 2y − 2z = 4
2x − 3y + 4z = −3
This can also be represented as,
Hence, x = 0, y = 5 and z = 3.
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