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3. Let T: R² → R² be a linear transformation, and suppose [7], the standard matrix representation of T, is given by 7-21 (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 S o T.

3. Let T: R² → R² be a linear transformation, and suppose [7], the standard matrix representation of T, is given by 7-21 (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 S o T.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 26EQ
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3. Let T: R² → R² be a linear transformation, and suppose [7], the standard matrix representation of T, is given by 7-21 (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 S o T.
Transcribed Image Text:3. Let T: R² → R² be a linear transformation, and suppose [7], the standard matrix representation of T, is given by 7-21 (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 S o T.
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