# Elementary Linear Algebra (matrix)

1. Sep 10, 2007

### dazedoutpinoy

1. The problem statement, all variables and given/known data
Determine the reduced row echolon form of

| cos(x) sin(x) |
| -sin(x) cos(x) |

2. Relevant equations
you can interchange any two rows or columns, multiply a row or column by a nonzero number, add a multiple of one row or column to another

3. The attempt at a solution
|1 0|
|0 1|

is the solution but i couldn't figure out how to apply trig functions to equal 1 on the matrix

2. Sep 10, 2007

### Timo

Ok, first off: I don't know what a "row echolon form" is. But using your calculation rules it is possible to obtain the identity.
What you first need to do (more specifically: What I had to do for my solution) is a case branching:

Case 1: sin(x) = 0:
Ok, I don't have to comment on this one, do I?

Case 2: cos(x) =0:
Your matrix is ((0,-1),(1,0)) (where I noted the two column-vectors in the inner parentheses). Using your modification rules you should easily get to the identity from there.

Case 3: Neither the sine nor the cosine term equal zero:
It's a few more steps but not too many. Two hints:
- cos(x) and sin(x) are non-zero numbers now, meaning you can (and actually must) multiply and divide by these terms.
- cos²(x) + sin²(x) = 1.

Last edited: Sep 10, 2007