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
ANSWERED
asked 2021-05-21

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.

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

Expert Answers (2)

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
\(x_1=8+7t, x_2=2-3t, x_3=-5-t, x_4=t\)

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Best answer
2021-10-13

Answer is given below (on video)

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