Linear Algebra Question

Question

Let T: R2→R2 be the linear transformation that first rotates points clockwise through 30∘ and then reflects points through the line y=x. Find the standard matrix A for T.

 

A = [] ?

Answer 1

A = R_y=xR_30°CW

   = ⌈0    1⌉ ⌈√3/2    1/2⌉

      ⌊1    0⌋ ⌊−1/2  √3/2⌋

  = ⌈−1/2 √3/2⌉

     ⌊√3/2   1/2⌋