The number of solution of the system of equations: `2x+y-z=7` `x-3y+2z=1,` is `3x+2y+k z=4` has a unique solution if `k!=0` (b) `-1

Explanation

To determine the number of solutions of the given system of equations and the conditions under which it has a unique solution, we can use the concept of determinants from linear algebra. We will set up the equations and find the determinant of the coefficient matrix.

### Given Equations:
1. \( 2x + y - z = 7 \) (Equation 1)
2. \( x - 3y + 2z = 1 \) (Equation 2)
3. \( 3x + 2y + kz = 4 \) (Equation 3)

### Step 1: Write the Coefficient Matrix
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