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Question
Examine the consistency of the system of equations.
5x − y + 4z = 5
2x + 3y + 5z = 2
5x − 2y + 6z = −1
Solution
5x - y + 4z = 5
2x + 3y + 5z = 2
5x - 2y + 6z = - 1
`[(5,-1,4),(2,3,5),(5,-2,6)] [(x),(y),(z)] = [(5),(2),(-1)]`
AX = B`abs A = [(5,-1,4),(2,3,5),(5,-2,6)]`
`= 5 (18 + 10) + 1 (12 - 25) + 4(-4 - 15)`
`= 140 - 13 - 76`
`= 51 ne 0`
Hence, equations are consistent with a unique solution.
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