For each of the following linear operators on R2, find the matrix representation of the transformation with respect to the homogeneous coordinate system: (a) The transformation L that rotates each vector by 120◦ in the counterclockwise direction (b) The transformation L that translates each point 3 units to the left and 5 units up (c) The transformation L that contracts each vector by a factor of one-third (d) The transformation that reflects a vector about the y-axis and then translates it up 2 units
For each of the following linear operators on R2, find the matrix representation of the transformation with respect to the homogeneous coordinate system: (a) The transformation L that rotates each vector by 120◦ in the counterclockwise direction (b) The transformation L that translates each point 3 units to the left and 5 units up (c) The transformation L that contracts each vector by a factor of one-third (d) The transformation that reflects a vector about the y-axis and then translates it up 2 units
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 21CR: Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find...
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Question
For each of the following linear operators on R2,
find the matrix representation of the transformation
with respect to the homogeneous
system
(a) The transformation L that rotates each
by 120◦ in the counterclockwise direction
(b) The transformation L that translates each point
3 units to the left and 5 units up
(c) The transformation L that contracts each vector
by a factor of one-third
(d) The transformation that reflects a vector about
the y-axis and then translates it up 2 units
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