Write the given matrix equation as a system of linear equations without matrices. begin{bmatrix}-1 & 0&1 0 & -1 &0 0&1&1 end{bmatrix}begin{bmatrix}x y z end{bmatrix}=begin{bmatrix}-4 2 4 end{bmatrix}

Write the given matrix equation as a system of linear equations without matrices. begin{bmatrix}-1 & 0&1 0 & -1 &0 0&1&1 end{bmatrix}begin{bmatrix}x y z end{bmatrix}=begin{bmatrix}-4 2 4 end{bmatrix}

Question
Matrices
asked 2021-02-26
Write the given matrix equation as a system of linear equations without matrices.
\(\begin{bmatrix}-1 & 0&1 \\ 0 & -1 &0 \\ 0&1&1 \end{bmatrix}\begin{bmatrix}x \\ y \\ z \end{bmatrix}=\begin{bmatrix}-4 \\ 2 \\ 4 \end{bmatrix}\)

Answers (1)

2021-02-27
Step 1
Given equation in matrix form:
\(\begin{bmatrix}-1 & 0&1 \\ 0 & -1 &0 \\ 0&1&1 \end{bmatrix}\begin{bmatrix}x \\ y \\ z \end{bmatrix}=\begin{bmatrix}-4 \\ 2 \\ 4 \end{bmatrix}\)
Step 2
Simplifying:
\(\begin{bmatrix}-1 & 0&1 \\ 0 & -1 &0 \\ 0&1&1 \end{bmatrix}\begin{bmatrix}x \\ y \\ z \end{bmatrix}=\begin{bmatrix}-4 \\ 2 \\ 4 \end{bmatrix}\)
\(\begin{bmatrix}-1 \cdot x+ 0\cdot y +1\cdot z \\ 0\cdot x -1 \cdot y + 0 \cdot z \\ 0 \cdot x + 1\cdot y +1 \cdot z \end{bmatrix}=\begin{bmatrix}-4 \\ 2 \\ 4 \end{bmatrix}\)
\(\begin{bmatrix}-x+z \\ -y \\ y+z \end{bmatrix}=\begin{bmatrix}-4 \\ 2 \\ 4 \end{bmatrix}\)
Comparing both matrices:
The system of linear equations formed:
\(-x+z=-4\)
\(-y=2\)
\(y+z=4\)
0

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