Questions: 3x + 3y + 12z = 9 3x + 2y + 10z = 6 2x + 4y + 17z = 7

Solution Steps

To solve the given system of linear equations, we can use matrix operations. Specifically, we can represent the system as a matrix equation \(AX = B\) and solve for \(X\) using matrix inversion or other suitable methods.

1. Represent the system of equations in matrix form \(AX = B\).
2. Use a suitable method (e.g., numpy's linalg.solve) to solve for \(X\).

The given system of equations can be represented as follows: \[ \begin{align_} 3x + 3y + 12z &= 9 \quad (1) \\ 3x + 2y + 10z &= 6 \quad (2) \\ 2x + 4y + 17z &= 7 \quad (3) \end{align_} \]

We can express the system in matrix form \(AX = B\), where: \[ A = \begin{bmatrix} 3 & 3 & 12 \\ 3 & 2 & 10 \\ 2 & 4 & 17 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}, \quad B = \begin{bmatrix} 9 \\ 6 \\ 7 \end{bmatrix} \]

By solving the matrix equation, we find: \[ X = \begin{bmatrix} 2 \\ 5 \\ -1 \end{bmatrix} \] This implies: \[ x = 2, \quad y = 5, \quad z = -1 \]

Final Answer