Question

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is co

Forms of linear equations
ANSWERED
asked 2021-06-04

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.

\(\begin{bmatrix}1 & -2&0 & -4 \\0 & 0&1 & 3\\0 & 0&0 & 0 \end{bmatrix}\)

Answers (1)

2021-06-05

\(x_1-2x_2=4\)
\(x_3=3\)
\(0=0\)
\(x_1=4+2x_2\)
\(x_2\), free
\(x_3=3\)
\(x_1=4+2t\)
\(x_2=t\)
\(x_3=3\)
\(x=\begin{bmatrix}4 \\0\\3 \end{bmatrix}+t\begin{bmatrix}2 \\1\\0 \end{bmatrix}\)

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