Sun K.

What are those matrices?

This 4 by 4 matrix will need elimination matrices E21 and E32 and E43. What are those matrices?
A=[2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2].

The first row is 2, -1, 0, 0.
The second row is -1, 2, -1, 0.
The third row is 0, -1, 2, -1.
The fourth row is 0, 0, -1, 2.

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Jonathan W. answered • 11/13/13

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Sun K.

How did you get the matrix [1, 0, 0, 0, 1/2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]?

The first row is 1, 0, 0, 0.
The second row is 1/2, 1, 0, 0.
The third row is 0, 0, 1, 0.
The fourth row is 0, 0, 0, 1.

And what do you mean by left multiply? How did you do it?
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11/13/13

Jonathan W.

I wrote a comment to answer your comment, but when I clicked "Save comment" it disappeared.
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11/15/13

Jonathan W.

It disappeared probably because I'm not allowed to include links, and I included a link to the paper I found the idea in.  That's University of Utah Math 2270 - Lecture 7: Elimination Using Matrices by Dylan Zwick, Fall 2012.  He starts with an example matrix that subtracts 2 times the first row from the second.  Using that idea, I came up with this:

[  1   0   0   0 ]  [  2  -1   0   0 ]       [  2  -1   0   0 ]
[ 1/2 1   0   0 ]  [ -1   2  -1   0 ]  =  [  0  3/2 -1  0 ]
[  0   0   1   0 ]  [  0  -1   2  -1 ]      [  0  -1   2  -1 ]
[  0   0   0   1 ]  [  0   0  -1   2 ]      [  0   0  -1   2 ]

So the matrix A you gave me is multiplied on the left by the elimination matrix I came up with.  That adds 1/2 times the first row of A to the second row of A, getting rid of that first -1.
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11/15/13

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