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प्रश्न
Examine the consistency of the system of equations.
5x − y + 4z = 5
2x + 3y + 5z = 2
5x − 2y + 6z = −1
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उत्तर
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
Now, |A| = `|(5,-1,4),(2,3,5),(5,-2,6)|`
= 5(18 + 10) + 1(12 − 25) + 4(−4 − 15)
= 140 − 13 − 76
= 51 ≠ 0
Hence, equations are consistent with a unique solution.
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