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

Vectors and spaces
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asked 2021-05-25

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. \(\begin{bmatrix}1 & -2&6 \\0 & 0&0 \end{bmatrix}\)

Answers (1)

2021-05-26

The augmented matrix does not contain a row in which the only nonzero entry appears in the last column. Therefore, this system of equations must be consistent.

Convert the augmented matrix into a system of equations.

\(x_1-2x_2=6\)
0=0

Solve for the leading entry for each individual equation. Determine the free variables, if any.
\(x_1=6+2x_2\)
\(x_2\), free

Parameterize the free variables.
\(x_1=6+2t\)
\(x_2=t\)

Write the solution in vector form.
\(x=\begin{bmatrix}6 \\0 \end{bmatrix}+t\begin{bmatrix}2 \\1 \end{bmatrix}\)

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