How can I reduce this matrix to its reduced row echelon form?

[doggitz]

I have to produce the reduced row echelon form of the following matrix:

A  =     |  cos(x)       sin(x)  |
         |  -sin(x)      cos(x)  |

I am just learning Linear Algebra, and I am in the early Chapters of my book, so I can only use the Gauss method or the Gauss-Jordan method for this matrix. Just to clarify, I am hoping to return to school, so I am trying to learn this on my own.


I believe the solution to be the I₂ identity matrix:

I  =      |  1        0  | 
         |  0        1  |

I have found the matrix A raised to a power of n, during previous exercises, where I had to use the double angle formulas for sin(x) and cos(x). Is this the same method/avenue to use when solving this problem?

 

[Dick]

No, you just do the same sort of thing you'd do if the matrix were full of numbers. Start out by multiplying the first row by sin(x) and add it to cos(x) times the second row.