   Chapter 11.1, Problem 14E ### 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
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 3 − 3 0 1 5 ]

To determine

(a)

Whether the matrix  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 .

Here, the leading entry is 1, first non zero number in row is 1 and the leading entry in each row is to the right in the row immediately above it

To determine

(b)

Whether the matrix  is in reduced row-echelon form.

To determine

(c)

To write:

The system of equations for the matrix .

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