Question

Examine the consistency of the system of equations.

5x − y + 4z = 5

2x + 3y + 5z = 2

5x − 2y + 6z = −1

Answer 1

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.