It can be proved that if A is 2 x 2 matrix with det(A)and such that the column vectors of A are orthogonal and have
length 1, then multiplication by A is a rotation through some angle theta . Verify that A=
[ -1/square root of2 -1/square rootof2
-1/square root of2 -1/square rootof2]

satisfies the stated conditions and find the angle of rotation.
27.

Question

It can be proved that if A is 2 x 2   matrix with  det(A)and such that the column vectors of A are orthogonal and have
length 1, then multiplication by A is a rotation through some angle theta . Verify that A=
[ -1/square root of2  -1/square rootof2
-1/square root of2  -1/square rootof2]
                  
satisfies the stated conditions and find the angle of rotation.
27.

anonymous · Answer

unfortunately i dont know how to do this from scratch, im kinda cheating because i know the rotation matrix is:
  cosx   -sinx
  sinx     cosx
where x is the angle of  rotation.

anonymous · Answer

should the bottom left entry be negative? or is it really positive?

anonymous · Answer

[ -1/square root of2 -1/square rootof2 
1/square root of2 -1/square rootof2] it is the matrix

anonymous · Answer

Well the angle is 45 degrees. Because sin(x) and cos(x) give 1/sqrt(2) or sqrt(2)/2 with 45 degrees. However, I concur with joe, I do not know how to do this from scratch.

anonymous · Answer

det(A)=1