Question

First recall that the matrix corresponding to a rotation by an angle ? is given by R_? = [cos(?) -sin(?) sin(?) cos(?)] Build a 2-by-2 matrix by first rotating by ?1 = - ? / 3, then stretching using the diagonal matrix D = [3 0; 0 1], then rotating again by ?2 = ? / 4 A = R_?2 D R_?1 = [ [ ] [ ] [ ] [ ] ]

          First recall that the matrix corresponding to a rotation by an angle ? is given by

R_? = [cos(?) -sin(?)
sin(?) cos(?)]

Build a 2-by-2 matrix by first rotating by ?1 = - ? / 3, then stretching using the diagonal matrix D = [3 0; 0 1], then rotating again by ?2 = ? / 4

A = R_?2 D R_?1 = 
[ [ ] [ ]
  [ ] [ ] ]

First recall that the matrix corresponding to a rotation by an angle ? is given by

R? = [cos(?) -sin(?)
sin(?) cos(?)]

Build a 2-by-2 matrix by first rotating by ?1 = - ? / 3, then stretching using the diagonal matrix D = [3 0; 0 1], then rotating again by ?2 = ? / 4

A = R?2 D R?1 =
[ [ ] [ ]
[ ] [ ] ]

Added by Theodore P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Thanks for your feedback!

First, recall that the matrix corresponding to a rotation by an angle θ is given by: cos(θ) -sin(θ) sin(θ) cos(θ) Now, let's build a 2-by-2 matrix by first rotating by θ1, then stretching using the diagonal matrix D, and finally rotating again by θ2. The resulting matrix A can be calculated as follows: A = Rot(θ1) D Rot(θ2)