# Answer to Question #1452 in Linear Algebra for AA

Question #1452

A = 4 2

-5 -2

Find an invertible 2x2 matrix Q such that Q^-1AQ is equal to a rotation followed by scaling by a positive real number, and write down both the rotation matrix and the scaling matrix. What is the angle of rotation of the matrix?

-5 -2

Find an invertible 2x2 matrix Q such that Q^-1AQ is equal to a rotation followed by scaling by a positive real number, and write down both the rotation matrix and the scaling matrix. What is the angle of rotation of the matrix?

Expert's answer

Rotation M = Scaling M

cos(theta) -sin(theta) = s

sin(theta) cos(theta) = 0 s

Thus

Q= 1 0

0 1

Scalling matrix is the same as well as rotation matrix. As cos(theta) = 1, rotation angle is equal to zero.

cos(theta) -sin(theta) = s

_{x}0sin(theta) cos(theta) = 0 s

_{y}Thus

Q= 1 0

0 1

Scalling matrix is the same as well as rotation matrix. As cos(theta) = 1, rotation angle is equal to zero.

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment