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Homework Help: Elementary Linear Algebra (matrix)

  1. Sep 10, 2007 #1
    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. jcsd
  3. Sep 10, 2007 #2
    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.
    - cosĀ²(x) + sinĀ²(x) = 1.
    Last edited: Sep 10, 2007
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