3. For each of the following matrices, draw the image of the unit square under the transforma- tion defined by that matrix. Then describe the transformation as a contraction/expansion, reflection, rotation, shear, or projection. (b) (c)

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Section 1.9
1. Assume that T is a linear transformation. Find the standard matrix of T.
(a) T: R2 R? rotates points about the origin through radians counter-clockwise.
(b) T:R2 R² reflects points across the x-axis, then reflects across the line y = x.
(c) T:R3 → R2 defined by T(x1, x2, T3) = (x1 – 5x2 +4x3, 12 - 6r3).
2. Is the transformation in 1 (c) one-to-one? Is it onto?
3. For each of the following matrices, draw the image of the unit square under the transforma-
tion defined by that matrix. Then describe the transformation as a contraction/expansion,
reflection, rotation, shear, or projection.
0.
(e)
(b) 6
(0)
Transcribed Image Text:Find Section 1.9 1. Assume that T is a linear transformation. Find the standard matrix of T. (a) T: R2 R? rotates points about the origin through radians counter-clockwise. (b) T:R2 R² reflects points across the x-axis, then reflects across the line y = x. (c) T:R3 → R2 defined by T(x1, x2, T3) = (x1 – 5x2 +4x3, 12 - 6r3). 2. Is the transformation in 1 (c) one-to-one? Is it onto? 3. For each of the following matrices, draw the image of the unit square under the transforma- tion defined by that matrix. Then describe the transformation as a contraction/expansion, reflection, rotation, shear, or projection. 0. (e) (b) 6 (0)
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