How would I prove the inverse of this matrice is as stated

1 1 1

1 2 3 is inverse of

1 3 6

3-3 1

-3 5-2

1-2 1

with working out if possible

Printable View

- Oct 12th 2006, 12:23 PMGreginverse matrices
How would I prove the inverse of this matrice is as stated

1 1 1

1 2 3 is inverse of

1 3 6

3-3 1

-3 5-2

1-2 1

with working out if possible - Oct 12th 2006, 12:25 PMTD!
Show that the product is equal to the unit matrix.

- Oct 12th 2006, 04:53 PMThePerfectHacker
- Oct 14th 2006, 03:31 AMTD!
If you're referring to having to check AB = I and BA = I, that's not true.

It's sufficient to show only one, if AB = I, then BA = I as well.

Although matrix multiplication doesn't commute in general, it does for A and its inverse. - Oct 14th 2006, 02:13 PMSoroban
Hello, Greg!

Since you are studying Inverses, I assume you know how to multiply.

What's stopping you?

Code:`| 1 1 1 | | 3 -3 1 |`

Prove that: | 1 2 3 | is the inverse of | -3 5 -2 |

| 1 3 6 | | 1 -2 1 |

Code:`| 1 1 1 | | 3 -3 1 |`

| 1 2 3 |.| -3 5 -2 |

| 1 3 6 | | 1 -2 1 |

| 1(3) + 1(-3) + 1(1) 1(-3) + 1(5) + 1(-2) 1(1) + 1(-2) + 1(1) |

= | 1(3) + 2(-3) + 3(1) 1(-3) + 2(5) + 3(-2) 1(1) + 2(-2) + 3(1) |

| 1(3) + 3(-3) + 6(1) 1(-3) + 3(5) + 6(-2) 1(1) + 3(-2) + 6(1) |

| 3 - 3 + 1 -3 + 5 - 2 1 - 2 + 1 |

= | 3 - 6 + 3 -3 + 10 - 6 1 - 4 + 3 |

| 3 - 9 + 6 -3 + 15 - 12 1 - 6 + 6 |

| 1 0 0 |

= | 0 1 0 |

| 0 0 1 |

Use the slide-bar to see the rest of line 2.

Edit: corrected the typo! - Oct 14th 2006, 03:52 PMAfterShock
I disagree.

| 1 0 1 |

| 0 1 0 |

| 0 0 1 |

Is not the identity matrix. A way to check this would be to augment the original Matrix with it's identity matrix and row reduce it to see what the inverse is.

That is, in this case,

M := Matrix([[3, -3, 1, 1, 0, 0], [-3, 5, -2, 0, 1, 0], [1, -2, 1, 0, 0, -1]])

(Using Maple notation). In which case, once that is row reduced, you get:

Matrix([[1, 0, 0, 1, 1, -1], [0, 1, 0, 1, 2, -3], [0, 0, 1, 1, 3, -6]])

The ABOVE matrix is the inverse matrix (in augmented columns), that is:

Matrix([[1, 1, -1], [1, 2, -3], [1, 3, -6]]) - Oct 15th 2006, 07:10 AMGregThanks for your help
I know this stuff is really easy, but I have not studied maths much and am doing a distance learning course, I really appreciate your help. It makes it a lot easier to understand when I see the working out. Thank you again

- Oct 15th 2006, 07:22 AMtopsquark
- Oct 15th 2006, 08:31 AMAfterShock
Indeed, that is because:

Matrix([[3, -3, 1, 1, 0, 0], [-3, 5, -2, 0, 1, 0], [1, -2, 1, 0, 0, -1]])

When I was row reducing that, I had a -1, where it should have been positive. My answer is correct if you simply change the sign of the last column.