Question

Use row reduction to find the inverse of the given matrix if it exists, and check your answer by multiplication. hint [see example 2.] (if the inverse doesn't exist, enter dne in all answer boxes.) 1 6 4 0 1 2 0 0 1

Answer 1

The given matrix is
| 1 6 4 |
| 0 1 2 |
| 0 0 1 |

Create the augmented matrix.
| 1 6 4 | 1 0 0 | R1
| 0 1 2 | 0 1 0 | R2
| 0 0 1 | 0 0 1 | R3

R1 -> R1 - 6*R2
| 1 0 -8 | 1 -6 0 | R1
| 0 1 2 | 0 1 0 | R2
| 0 0 1 | 0 0 1 | R3

R1 -> R1 + 8*R3
| 1 0 0 | 1 -6 8 | R1
| 0 1 2 | 0 1 0 | R2
| 0 0 1 | 0 0 1 | R3

R2 -> R2 - 2*R3
| 1 0 0 | 1 -6 8 |
| 0 1 0 | 0 1 -2 |
| 0 0 1 | 0 0 1 |

The inverse is
| 1 -6 8 |
| 0 1 -2 |
| 0 0 1 |

Verification:
| 1 6 4 | | 1 -6 8 | | 1 0 0 |
| 0 1 2 | | 0 1 -2 | = | 0 1 0 |
| 0 0 1 | | 0 0 1 | | 0 0 1 |