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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
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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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
Transcribed Image Text: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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