Chapter 11.2, Problem 90AYU

When solving a system of linear equations using matrices, do you prefer to place the augmented matrix in row echelon form or in reduced row echelon form? Give reasons for your choice.

To determine

To find: Give reasons for your choice.

Answer to Problem 90AYU

See explanation.

Explanation of Solution

Given:

When solving a system of linear equations using matrices, do you prefer to place the augmented matrix in row echelon form or in reduced row echelon form.

Calculation:

Easy to solve the method for row echelon form.

Row-Echelon Form

A matrix is said to be in row-echelon form if

1. All rows consisting entirely of zeros are at the bottom.
2. In each row, the first non-zero entry form the left is a 1, called the leading 1.
3. The leading 1 in each row is to the right of all leading 1's in the rows above it.

If, in addition, each leading 1 is the only non-zero entry in its column, then the matrix is in reduced row-echelon form.

It can be proven that every matrix can be brought to row-echelon form (and even to reduced row-echelon form) by the use of elementary row operations. At that point, the solutions of the system are easily obtained.

In the following example, suppose that each of the matrices was the result of carrying an augmented matrix to reduced row-echelon form by means of a sequence of row operations.