Consider the following. Tis the clockwise rotation (e is negative) of 60° in R, v - (1, 6). (a) Find the standard matrix A for the linear transformation T. A- (b) Use A to find the image of the vector v. T(v) - (c) Sketch the graph of v and s image. I(v) 7-6-5-4-3-2-1 T() -7 -6-5-4-3-2-1, 1 2 34567 -7-6-5-4-3-2-1 7(v) -4 -5 -6 -7 -5

Consider the following. Tis the clockwise rotation (e is negative) of 60° in R, v - (1, 6). (a) Find the standard matrix A for the linear transformation T. A- (b) Use A to find the image of the vector v. T(v) - (c) Sketch the graph of v and s image. I(v) 7-6-5-4-3-2-1 T() -7 -6-5-4-3-2-1, 1 2 34567 -7-6-5-4-3-2-1 7(v) -4 -5 -6 -7 -5

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the following.
Tis the clockwise rotation (e is negative) of 60° in R2, v = (1, 6).
(a) Find the standard matrix A for the linear transformation T.
A =
(b) Use A to find the image of the vector v.
T(v) =
(c) Sketch the graph of v and its image.
I(V)
7 -6-5-4 -3-2-1/ 1 2 345 67
T(V)
T()
2-5-4-3-2-1.
-7 -6-5-4-3 -2-1, N 34567"
-2
-5

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