   Chapter 2.2, Problem 13E

Chapter
Section
Textbook Problem

In Exercises 9 − 18 , indicate whether the matrix is in row-reduced form. [ 1 0 0 0 1 0 0 0 1   |   3 4 5 ]

To determine

To find:

Whether the given matrix is in row-reduced form.

[100010001|345]

Explanation

Approach:

The conditions of the row-reduced form of the matrix are as follows,

1. Each row consisting entirely of zeros lies below all rows having nonzero entries.

2. The first nonzero entry in each (nonzero) row is 1 (called a leading 1).

3. In any two successive (nonzero) rows, the leading 1 in the lower row lies to the right of the leading 1 in the upper row.

4. If a column in the coefficient matrix contains a leading 1, then the other entries in that column are zeros.

Calculation:

Consider the matrix,

[1000100

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