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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3. Let T: R2 R2 be a linear transformation, and suppose [T], the standard matrix representation
of T, is given by
7 = 2 i
(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.
Transcribed Image Text:3. Let T: R2 R2 be a linear transformation, and suppose [T], the standard matrix representation of T, is given by 7 = 2 i (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.
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