Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to find the matrix of a linear transformation which rotates every vector in R² by a given angle.

Q1:

Find the matrix for the linear transformation that rotates every vector in β 2 through an angle of π 3 .

Q2:

Find the matrix for the linear transformation that rotates every vector in β 2 through an angle of π 4 .

Q3:

Find the matrix for the linear transformation which rotates every vector in β 2 through an angle of π 1 2 .

Q4:

Find the matrix for the linear transformation which rotates every vector in β 2 through an angle of 2 π 3 .

Q5:

Find the matrix for the linear transformation which rotates every vector in β 2 through an angle of 5 π 1 2 .

Q6:

Find the matrix for the linear transformation which rotates every vector in β 2 through an angle of β π 3 .

Q7:

Find, with respect to the standard basis, the matrix which rotates every vector in counterclockwise about the origin through an angle of .

Q8:

Q9:

Q10:

Find, with respect to the standard basis, the matrix which rotates every vector in β 2 counterclockwise about the origin through an angle of 5 π 1 2 .

Q11:

Describe the geometric effect of the transformation produced by the matrix β β β β β β 2 2 β β 2 2 β 2 2 β 2 2 β β β β β .

Q12:

A rotation with centre the origin sends the vector οΌ 3 4 ο to οΌ 4 3 ο . Find the matrix representation of this rotation.

Q13:

Let π΄ be the matrix of the transformation which rotates all vectors in β 2 through an angle of π , where 0 < π β€ 2 π . For which values of π does π΄ have a real eigenvalue?

Q14:

Consider the linear map π βΆ β β β 2 2 , which acts by rotating a vector π β counterclockwise around the origin. Which of the following is the matrix of the linear transformation?

Q15:

Consider the linear transformation , which rotates each vector 90 degrees counterclockwise about the positive -axis then 45 degrees counterclockwise about the positive -axis. Find the matrix representation of in the standard basis.

Q16:

Consider the linear transformation , which rotates each vector 45 degrees counterclockwise about the positive -axis then 90 degrees counterclockwise about the positive -axis. Find in the standard basis.

Donβt have an account? Sign Up