Chapter 11.1, Problem 17E

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

Chapter
Section

### Algebra and Trigonometry (MindTap ...

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

# 1 3 - 2 0 Form of a Matrix A matrix is given. (a) Determine whether the matrix is in row-echelon form. (b) Determine whether the matrix is in reduced row-echelon form. (c) Write the system of equations for which the given matrix is the augmented matrix. [ 1 0 0 0 0 0 0 0 0 1 5 1 ]

To determine

(a)

Whether the matrix [100000000151] is in row-echelon form.

Explanation

Approach:

A matrix is in row echelon form if it satisfies the following conditions:

1. The first non zero number in each row is 1. Non zero number is called leading entry.

2. The leading entry in each row is to right of the leading entry in the row immediately above it.

3. All rows consisting entirely of zeroes are at the bottom of the matrix.

Calculation:

Consider the augmented matrix [100000000151].

Based on the above explanation, the leading entry in each row is not 1

To determine

(b)

Whether the matrix [100000000151] is in reduced row-echelon form.

To determine

(c)

To write:

The system of equations for the matrix [100000000151].

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