Questions: x-y+z-w=1 y+2 z+w=1 -z+w=3 -x+2 y-3 z+5 w=1 x=, y=, z=, w=

Solution Steps

To solve this system of linear equations, we can use matrix operations. First, represent the system as an augmented matrix. Then, apply Gaussian elimination or use a built-in solver to find the values of the variables \(x\), \(y\), \(z\), and \(w\).

The given system of linear equations is: \[ \begin{align_} x - y + z - w &= 1 \\ y + 2z + w &= 1 \\ -z + w &= 3 \\ -x + 2y - 3z + 5w &= 1 \end{align_} \]

We represent the system as an augmented matrix: \[ \begin{bmatrix} 1 & -1 & 1 & -1 & | & 1 \\ 0 & 1 & 2 & 1 & | & 1 \\ 0 & 0 & -1 & 1 & | & 3 \\ -1 & 2 & -3 & 5 & | & 1 \end{bmatrix} \]

Using matrix operations, we solve for the variables \(x\), \(y\), \(z\), and \(w\). The solution to the system is: \[ \begin{align_} x &= -22.00 \\ y &= -26.00 \\ z &= 8.000 \\ w &= 11.00 \end{align_} \]

Final Answer