Question

The following simultaneous equations:

x + y + z = 3

x + 2y + 3z = 4

x + 4y + kz = 6

Will not have a unique solution for k equal to

1. 7
2. 6
3. 0
4. 5

Answer 1

Correct Answer - Option 1 : 7

Concept:

For unique solution:

Determinant of A, |A|≠ 0

where A is any matrix

Calculation:

\(D = \begin{vmatrix} 1 &1 &1 \\ 1&2&3 \\ 1 &4 &k \end{vmatrix}\)

|A| ≠ 0

⇒ 1 (2k - 12) - (k - 3) + 1 (4 - 2) = 0

⇒ k - 7 = 0

⇒ k = 7

So, The following simultaneous equations will not have a unique solution for k equal to 7