Question

Write the vector form of the general solution of the given system of linear equations.x1+2x2−x3+x4=0

Forms of linear equations
ANSWERED
asked 2021-06-24

Write the vector form of the general solution of the given system of linear equations.
\(x_1+2x_2−x_3+x_4=0\)

Answers (1)

2021-06-25

\([1,2,-1,1,0]\) Write the augmented matrix of the coefficients and constants
\([1,2,-1,1,0]\) Transform the matrix in its reduced row echelon form.
\(x_1=-2x_2+x_3-x_4\)
\(x_2=x_2\) free
\(x_3=x_3\) free
\(x_4=x_4\) free
Determine the general solution

Rewrite the solution in vector form
\(\begin{bmatrix}x_1 \\x_2\\x_3\\x_4 \end{bmatrix}=x_2\begin{bmatrix}-2 \\1\\0\\0\end{bmatrix}+x_3\begin{bmatrix}1 \\0\\0\\0\end{bmatrix}-x_4\begin{bmatrix}-1 \\0\\0\\1\end{bmatrix}\)

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