What is the rank of an nxn matrix and how is it determined?

[JonathanT]

Homework Statement

http://img94.imageshack.us/img94/5227/nxnmatrix.png

Homework Equations

Rank(A) = the number of pivots in Matrix A.

The Attempt at a Solution

I've spent some time rewriting the matrix and other operations. I really just feel like I'm banging my head against the wall. Not making any progress. Just need to be pointed in the right direction. Oh and the answer is "2." No idea how they get that. Thanks for any help in advance.

Edit: For reference this problem is from Applied Linear Algebra by Olver. Problem 1.8.17.

 

[STEMucator]

Homework Statement

http://img94.imageshack.us/img94/5227/nxnmatrix.png

Homework Equations

Rank(A) = the number of pivots in Matrix A.

The Attempt at a Solution

I've spent some time rewriting the matrix and other operations. I really just feel like I'm banging my head against the wall. Not making any progress. Just need to be pointed in the right direction. Oh and the answer is "2." No idea how they get that. Thanks for any help in advance.

Stop and ask yourself how many linearly independent columns compose your matrix A.

If that notion confuses you, ask yourself how many zero ROWS you have after row reduction...

 

[JonathanT]

I think I get it. I was reducing the matrix wrong. I think I have the correct rref of the matrix now. Take a look and let me know what you think.

Solution