http://i1097.photobucket.com/albums/...s_/Problem.jpg

I don't quite understand how to use that augmented matrix to prove anything about a, b and c.

Any ideas on where to start?

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- Jan 11th 2011, 05:43 PMTN17Matrices - Linear equations
http://i1097.photobucket.com/albums/...s_/Problem.jpg

I don't quite understand how to use that augmented matrix to prove anything about a, b and c.

Any ideas on where to start? - Jan 11th 2011, 07:40 PMTN17
The above image seems a bit hard to read.

Here is another question similar in format, though, and it's clearer:

http://i1097.photobucket.com/albums/...sics_/help.jpg

It's part of ourbut I'm not sure how to incorporate that into this question.__matrices unit__ - Jan 11th 2011, 08:09 PMProve It
25. You know four points that lie on the curve, .

So that means they all satisfy the equation .

So

.

So now you can set up your matrix equation...

- Jan 11th 2011, 08:25 PMTN17
.I usually write the constants in the same brackets as the large matrix here (to the furthest right side of the matrix, since that's what we were taught). So:

0 0 0 1 10

1 1 1 1 7

27 9 3 1 -11

64 16 4 1 -14

Is that right?

Would I use Gauss-Jordan to reduce that into reduced row-echelon?

I'm still confused about how to find the variables from there. - Jan 11th 2011, 08:38 PMTN17
.

- Jan 12th 2011, 07:44 AMHallsofIvy
[QUOTE=TN17;604092].I usually write the constants in the same brackets as the large matrix here (to the furthest right side of the matrix, since that's what we were taught). So:

0 0 0 1 10

1 1 1 1 7

27 9 3 1 -11

64 16 4 1 -14

Is that right?/[quote]

Yes, that is what is meant by the "augmented" matrix.

Quote:

Would I use Gauss-Jordan to reduce that into reduced row-echelon?

I'm still confused about how to find the variables from there.

Then subtract 27 times the first row from the second, 64 times the first row from the third, etc. - Jan 12th 2011, 07:31 PMProve It
If you have a CAS, it's quite simple if you know that the solution to the matrix equation

is

... - Jan 13th 2011, 09:22 AMHallsofIvy
- Jan 13th 2011, 02:28 PMProve It
- Jan 13th 2011, 02:40 PMpickslides
I'll meet you guys halfway. To maximise understanding the OP should know how to solve a system like the one above by hand. Once confident with such methods then use technology to save time.