Question

The system of simultaneous linear equations kx + 2y – z = 1,  (k – 1)y – 2z = 2 and (k + 2)z = 3 have a unique solution if k equals:

Options

• – 1

• – 2

• 0

• 1

Answer 1

– 1

Explanation:

The matrix form of the given system of equation is:

`[(k, 2, -1),(0, k - 1, -2),(0, 0, k + 2)] [(x),(y),(z)] = [(1),(2),(3)]`

As a result, if the coefficient matrix is determinant, it will have a solution ≠ 0

i.e. (k – 1)(k + 2)  ≠ 0

i.e., k ≠ 0, 1, – 2

As a result, the given system of equations will only have a solution at k = – 1.