Suppose T is a transformation from <mi mathvariant="double-struck">R 2 </m

uplakanimkk

uplakanimkk

Answered question

2022-07-14

Suppose T is a transformation from R 2 to R 2 . Find the matrix A that induces T if T is the (counter-clockwise) rotation by 3 4 π.
how to begin to find a matrix that is 2x2 for this question.

Answer & Explanation

Dayana Zuniga

Dayana Zuniga

Beginner2022-07-15Added 16 answers

The rotation matrix is [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] But blindly applying this formula doesn't teach you the most important part of linear transformations. (ANY linear transformation matrix is defined by where it takes the unit vectors.)
This linear transformation T that is a counterclockwise rotation takes [ 1 0 ] to [ cos ( θ ) sin ( θ ) ] and [ 0 1 ] to [ sin ( θ ) cos ( θ ) ] . You can confirm this on your own using geometry.
And this works for ANY linear transformation.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?