Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation on this face.
By an angle of , the face gets rotated clockwise.
Let the matrix be,
The matrix is,
Now, graph the obtained vectors on the given circular face.
Hence, is obtained by rotating the vector through an angle of in the clockwise direction.
Give a geometric interpretation of the linear transformations defined by the matrices in Exercises 16 through 23 . Show the effect of these transformations on the letter considered in Example 5 . In each case, decide whether the transformation is invertible. Find the inverse if it exists, and interpret it geometrically. See Exercise 13 .
94% of StudySmarter users get better grades.Sign up for free