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# Matrix Row Operations and Inverses Help (page 2)

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By McGraw-Hill Professional
Updated on Oct 4, 2011

#### Example 1:

• Find the inverse matrix

The augmented matrix is

Step 1 Use Row 1 and Row 2 to make the D entry a 0 by computing −2 Row 1 + Row 2.

Step 2 Use Row 1 and Row 3 to make the G entry a 0 by computing −4 Row 1 + Row 3.

Step 3

Step 4 This step is not necessary because the B entry is already 0. New Row 1 is old Row 1.

Step 5 Use Row 2 and Row 3 to make the H entry a 0 by computing Row 2 + Row 3.

Step 6

Step 7 Use Row 1 and Row 3 to make the C entry a 0 by computing 10 Row 1 + Row 3.

Step 8 Use Row 2 and Row 3 to make the F entry a 0 by computing −2 Row 2 + Row 3.

Step 9

Step 10 Divide the Row 1 by 10, the Row 2 by −4, and Row 3 by 10 to get the next matrix.

The inverse matrix is

#### Example 2:

• Find the inverse matrix.

The augmented matrix is

Step 1 Use Row 1 and Row 2 to make the 1 entry a 0.

Step 2 This step is not necessary because 0 is already in the G entry. New Row 3 is old Row 3.

Step 3

Step 4 This step is not necessary because the B entry is already 0. New Row 1 is old Row 1.

Step 5 Use Row 2 and Row 3 to make the 1 entry a 0.

Step 6

Step 7 Use Row 1 and Row 3 to make 2, the C entry, a 0.

Step 8 Use Row 2 and Row 3 to make 2, the F entry, a 0.

Step 9

Step 10 Divide Row 1 and Row 2 by 12 and Row 3 by −4.

The inverse matrix is

## Matrix Row Operations and Inverses Practice Problems

#### Practice

Find the inverse matrix.

#### Solutions

Step 1

Step 2

Step 3

Step 4 Divide Row 1 by 5.

Step 5 Divide Row 2 by 5.

Step 6

The inverse matrix is

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

To make the numbers smaller, replace Row 1 with Row 1 and Row 3 by Row 3.

Step 7

Step 8

Step 9

Step 10 Divide Row 1 by −520, Row 2 by 104, and Row 3 by 65.

Practice problems for this concept can be found at: Matrices Practice Test.

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