Question

solve the system of equations by gaussian elimination:
\\
\

$$\begin{cases} 2x - 4y + z = 1 \\\\ -x + y - z = 1 \\\\ x - 2y = 1 \\end{cases}$$

\\

\\(x = \\)
\\(y = \\)
\\(z = \\)

Explanation:

Step 1: Write the augmented matrix

$$
LATEXBLOCK0
$$

Step 2: Swap rows to get pivot

$$
LATEXBLOCK1
$$

Step 3: Eliminate first column entries

$$
LATEXBLOCK2
$$

Step 4: Solve for z

$$z = -3$$

Step 5: Solve for y

$$y = -1$$

Step 6: Solve for x

$$x = -1$$

Answer:

\(x = -1\)
\(y = -1\)
\(z = -3\)