Write the vector form of the general solution of the given system of linear equations. 3x_1+x_2-x_3+x_4=0 2x_1+2x_2+4x_3-6x_4=0 2x_1+x_2+3x_3-x_4=0

Question
Forms of linear equations
asked 2020-12-17
Write the vector form of the general solution of the given system of linear equations.
\(3x_1+x_2-x_3+x_4=0\)
\(2x_1+2x_2+4x_3-6x_4=0\)
\(2x_1+x_2+3x_3-x_4=0\)

Answers (1)

2020-12-18
\(\begin{bmatrix}3&1&-1&1&0\\2&2&4&-6&0\\2&1&3&-1&0\end{bmatrix}\)
Write the augmented matrix of the coefficients and constants
\(\begin{bmatrix}1&0&0&2&0\\0&1&0&-5&0\\0&0&1&0&0\end{bmatrix}\)
Transform the matrix in its reduced row echelon form.
\(x_1=-2x_4\)
\(x_2=5x_4\)
\(x_3=0\)
\(x_4=x_4 \text{ free}\)
Determine the general solution
\(\begin{bmatrix}x_1\\x_2\\x_3\\x_4\end{bmatrix}=x_4 \begin{bmatrix}-2\\ 5 \\ 0 \\ 1 \end{bmatrix}\)
Rewrite the solution in vector form
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