elementary matrices & G-J pivotting! help please!?

Question

how do i determine E, a product of elementary matrices which when premultiplying A performs Gauss-Jordan pivoting on the (2,2)-entry of A where:

A=

[1, -2, 1, 1]
[0, 6, -6, 12]
[0, 3, -12, 8]

(a 3x4 matrix)

thanks heaps for any help you can give me on this one!

Answer 1

To perform the Gauss-Jordan reduction on A_(2, 2), we would have to add 1/3 of row 2 to row 1, divide row 2 by 6, and subtract 1/2 of row 2 from row 3. This is equivalent to left-multiplying by the matrix:

[1, 1/3, 0]
[0, 1/6, 0]
[0, -1/2, 1]

Now, the real question: how do you determine this? The reason is that the entries in the nth row of the product are a linear combination of the rows of the second matrix, the coefficients of which are given by the entries of the nth row of the first matrix. Thus in this case, we are saying we want the first row of the product to be 1 times the first row of A + 1/3 times the second row of A, the second row to be 1/6 times the second row of A, and the third row to be 1 times the current third row of a -1/2 times the second row of A. When you think about it in that way, it should be obvious what numbers need to go where in E.

Answer 2

You wouldn't happen to go to the University of Adelaide would you?

It doesnt matter that it isnt a square matrix. Just do G-J elim. as usual. There will be free variables at the end but you dont have to go that far to get the answer

R2=R2+3R1
then R1 = R1+2R2 and R3=R3-3R2

Answer 3

extreme/low factors of our situations....yet, we outfitted this city out of rock and roll! good judgment in that chaotic university...i had to work out a alien deliver too, yet unfortunately, i'm going to easily look out my window on the friends. solid Morning!