The number of solution of the system of equations: `x+y+z=2` `2x+y-z=3,` is `3x+2y+k z=4` has a unique solution if `k!=0` (b) `-1 < k < 1` (c) `-2 < k < 2` (d) `k = 0`

Explanation

To determine the number of solutions of the given system of equations, we need to analyze the equations and their coefficients. The system of equations is:

1. \( x + y + z = 2 \)
2. \( 2x + y - z = 3 \)
3. \( 3x + 2y + kz = 4 \)

We can express this system in matrix form \( AX = B \), where \( A \) is the coefficient matrix, \( X \) is the variable matrix, and \( B \) is the constant matrix.

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