Question

# Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given reduced row echelon form. Solve the

Forms of linear equations

Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given reduced row echelon form. Solve the system. Assume that the variables are named $$x_1,x_2$$... from left to right.

$$\begin{bmatrix}1 & 0&0&-7&8 \\0 & 1&0&3&2 \\0 & 0&1&1&-5 \\ \end{bmatrix}$$

2021-05-22

The linear system corresponding to the augmented matrix is
$$x_1—7x_4=8$$
$$x_2+3x_4=2$$
$$x_3+x_4=—5$$
The lending variables are $$x_1, x_2$$ and $$x_3$$. Solve for the leading variables: $$x_1=8+7x_4$$
$$x_2=2-3x_4$$
$$x_3=—5—x_4$$
Assign arbitrary value to free variable $$x_4$$, say $$x_4 = t$$. Then the solution set is described by the parametric equations
$$x_1=8+7t, x_2=2-3t, x_3=-5-t, x_4=t$$

2021-10-13

Answer is given below (on video)