   Chapter 11.1, Problem 28E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 2 5 - 2 8 Back-Substitution A matrix is given in row-echelon form. (a) Write the system of equations for which the given matrix is the augmented matrix. (b) Use back-substitution to solve the system. [ 1 0 − 2 2 5 0 1 3 0 − 1 0 0 1 − 1 0 0 0 0 1 − 1 ]

To determine

(a)

To write:

The system of equations for the matrix .

Explanation

Approach:

A system of the linear equation can be transformed into the augmented matrix, by writing only the coefficients and constants that appear in the equations. The missing variable in the equation corresponds to a 0 entry in the augmented matrix.

Calculation:

Consider the augmented matrix .

The leading variables are x, y, z, and w.

The system of equations is x2z+2w=5, y+3z=1, zw=0, and w=1

To determine

(b)

To solve:

The system of equations for the matrix .

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