Using matrices, solve the following system of linear equations: x - y + 2z = 7, 3x + 4y - z = -1, 2x - y + 3z = 12

The given system of equations can be expressed and represented in matrix form as AX = B, where
A = ∣∣∣∣1 -1 2∣∣∣∣
∣∣∣∣3 4 -1∣∣∣∣
∣∣∣∣2 -1 3∣∣∣∣, X = ∣∣∣∣x∣∣∣∣
y∣∣∣∣
z∣∣∣∣, B = ∣∣∣∣7∣∣∣∣
∣∣∣∣-1∣∣∣∣
∣∣∣∣12∣∣∣∣
Now |A| = ∣∣∣∣1 -1 2∣∣∣∣
∣∣∣∣3 4 -1∣∣∣∣
∣∣∣∣2 -1 3∣∣∣∣ = 1(12 - 1) + 1(9 + 2) + 2(-3 - 8) = 11 + 11 - 22 = 0
Since |A| = 0, the system does not have a unique solution. The solution may be infinitely many solutions or no solution. Further analysis (e.g., row reduction) is needed to determine the nature of the solution set. The provided solution is incorrect as it assumes a non-zero determinant.