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

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

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
$$\begin{bmatrix}x_1 \\x_2\\x_3\\x_4 \end{bmatrix}=x_2\begin{bmatrix}-2 \\1\\0\\0\end{bmatrix}+x_3\begin{bmatrix}1 \\0\\0\\0\end{bmatrix}-x_4\begin{bmatrix}-1 \\0\\0\\1\end{bmatrix}$$