3. Let T: R² → R2 be a linear transformation, and suppose [T], the standard matrix representation of T, is given by [2] - [6] = (a) Sketch how the unit square corresponding to the vectors (1, 0) and (0,1) is transformed when applying T, and identify T as a particular geometrical transformation. (b) Specify S(1,0) and S(0, 1) for S: R2 R2 the linear transformation corresponding to reflection in the y-axis, and from this specify [S]. (c) With S and T as above, give a geometrical description of To SOT.

3. Let T: R² → R2 be a linear transformation, and suppose [T], the standard matrix representation of T, is given by [2] - [6] = (a) Sketch how the unit square corresponding to the vectors (1, 0) and (0,1) is transformed when applying T, and identify T as a particular geometrical transformation. (b) Specify S(1,0) and S(0, 1) for S: R2 R2 the linear transformation corresponding to reflection in the y-axis, and from this specify [S]. (c) With S and T as above, give a geometrical description of To SOT.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 39E: For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the...

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