Write the vector form of the general solution of the given system of linear equations. x_1+2x_2-x_3=0 x_1+x_2+x_3=0 x_1+3x_2-3x_3=0

Write the vector form of the general solution of the given system of linear equations. x_1+2x_2-x_3=0 x_1+x_2+x_3=0 x_1+3x_2-3x_3=0

Question
Forms of linear equations
asked 2020-12-28
Write the vector form of the general solution of the given system of linear equations.
\(x_1+2x_2-x_3=0\)
\(x_1+x_2+x_3=0\)
\(x_1+3x_2-3x_3=0\)

Answers (1)

2020-12-29
\(\begin{bmatrix}1&2&-1&0\\1&1&1&0\\1&3&-3&0\end{bmatrix}\)
Write the augmented matrix of the coefficients and constants
\(\begin{bmatrix}1&0&3&0\\0&1&-2&0\\0&0&0&0\end{bmatrix}\)
Transform the matrix in its reduced row echelon form.
\(x_1=-3x_3\)
\(x_2=2x_3\)
\(x_3=x_3 \text{ free}\)
Determine the general solution
\(\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=x_4 \begin{bmatrix}-3\\ 2 \\ 1 \end{bmatrix}\)
Rewrite the solution in vector form
0

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