IIT JEE Advanced 2008 Paper 1

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.