Questions: x+2y+0z=12 0x+3y-4z=25 x+6y+z=20

Solution Steps

The system of equations is represented in matrix form as \(AX = B\), where: $$ \begin{align_} A &= \begin{bmatrix} 1 & 2 & 0 \\ 0 & 3 & -4 \\ 1 & 6 & 1 \end{bmatrix}, X &= \begin{bmatrix} x \\ y \\ z \end{bmatrix}, B &= \begin{bmatrix} 12 \\ 25 \\ 20 \end{bmatrix} \end{align_} $$

The determinant of matrix \(A\) is 19.

Since the determinant is non-zero, the system has a unique solution. The solution is found using the inverse of matrix \(A\) to find \(X = A^{-1}B\). The solution is \(x = 6, y = 3, z = -4\).

Final Answer: