We have the system of equations: For these two items. x - 2y + 3z = - 1 - x + y - 2z = k x - 3y + 4z = 1 Therefore, Δ = |
1
−2
3
−1
1
−2
1
−3
4
| = 0 Δx = |
−1
−2
3
k
1
−2
1
−3
4
| = (3 - k) Δy = |
1
−1
3
−1
k
−2
1
1
4
| = (k - 3) Δz = |
1
−2
−1
−1
1
k
1
−3
1
| = (k - 3) Statement 1: If k ≠ 3, then Δ = 0 and Δx|Δy|Δz ≠ 0. Therefore, system of equation has no solution. Hence, Statement 1 is true. Statement 2 is true and it is the correct explanation of Statement 1.