Math Forum / Mathematics / Undergraduate Math / January 2006

This was a homework problem from Elementary Linear Algebra, Ninth Edition,
Howard Anton and Chris Rorres.  Can someone please check it for me.  I have
worked through it several times and gotten different answers.

Use Gauss-Jordan elimination to solve for x' and y' in terms of x and y.
                                                   x = x'cos(a) - y'sin(a)
                                                   y = x'sin(a) + y'cos(a)

First I established an augmented matrix: [ cos(a)    -sin(a) | x ]
                                                           [ sin(a)
cos(a) | y]

Then I said R1--> cos(a) * R1;  R2 --> sin(a) * R2:
s^2(a)    -sin(a)cos(a)    | x * cos(a)]
                                                                           
   [sin^2(a)      sin(a)cos(a)    | y * sin(a)  ]

So R1 --> R2 + R1: [ 1                      0            | x cos(a) + y
sin(a)]
                               [ sin^2(a)    sin(a)cos(a)    |        y
sin(a)          ]

Next, R2 --> -sin^2(a) R1 + R2:    [ 1           0                | x cos(a)
+ y sin(a)                                ]
                                                     [ 0    sin(a) cos(a)

So R2 --> 1/(sin(a)*cos(a)) * R2    [ 1    0 | x cos(a) + y
      ]
                                                      [ 0    1 | -x
sin(a) - y sin(a) tan (a) + y / cos (a) ]

I think this is right, but would like someone to double check it for me.
Thanks for your time.

Respectfully,
Dustin