2. d)

find a row operation that will restore the given elementary matrix to an identity matrix.

1 0 -1/7 0

0 1 0 0

0 0 1 0

0 0 0 1

I cannot solve this. I think I have to find an row operation that will make -1/7 become a 0. Please help.

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- Jan 27th 2010, 05:02 PMthekrown[SOLVED] Elementary matrix, restore to identity matrix
2. d)

find a row operation that will restore the given elementary matrix to an identity matrix.

1 0 -1/7 0

0 1 0 0

0 0 1 0

0 0 0 1

I cannot solve this. I think I have to find an row operation that will make -1/7 become a 0. Please help. - Feb 12th 2010, 08:04 PMthekrown
Am I allowed to multiply row I by 7 which gives

7 0 -1 0

0 1 0 0

0 0 1 0

0 0 0 1

then add row III to row I to get

7 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

then multiply row I by 1/7 to get

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

Correct? - Feb 13th 2010, 05:37 AMHallsofIvy
Yes. but that's not a single row operation.

This can be done by: Add 1/7 times the third row to the first row.

(In fact, an "elementary" matrix is defined as one that is created by applying a single row operation to the identity matrix. Here, this is an elementary matrix because it can be created by applying "subtract 1/7 times the third row from the first row" and, of course, you get back to the identity matrix by doing the opposite-**add**1/7 times the third row to the first row. - Feb 13th 2010, 10:04 AMthekrown
Gotcha. Thanks.