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Consider the following. 7 is the counterclockwise rotation of 120° in R², v = v = (2, 2), (a) Find the standard matrix A for the linear transformation 7. A = (b) Use A to find the image of the vector v. T(v) = (c) Sketch the graph of and its image. y 4 O -4 Ť (V) -2 -2 41 2 -2 2 T (V) X -4 -4 -2 T (V) -2 2 T(V) 2

Consider the following. 7 is the counterclockwise rotation of 120° in R², v = v = (2, 2), (a) Find the standard matrix A for the linear transformation 7. A = (b) Use A to find the image of the vector v. T(v) = (c) Sketch the graph of and its image. y 4 O -4 Ť (V) -2 -2 41 2 -2 2 T (V) X -4 -4 -2 T (V) -2 2 T(V) 2

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. 7 is the counterclockwise rotation of 120° in R2, v = (2, 2), (a) Find the standard matrix A for the linear transformation 7. A = (b) Use A to find the image of the vector v. T(v) = (c) Sketch the graph of vand its image. y 4 -4 T (V) -2 4 -2 y 4 2 -2 V 2 T (V) X -4 -4 -2 T (V) -2 y 4 2 -2 y 2 -2 T (V) 2 2
Transcribed Image Text:Consider the following. 7 is the counterclockwise rotation of 120° in R2, v = (2, 2), (a) Find the standard matrix A for the linear transformation 7. A = (b) Use A to find the image of the vector v. T(v) = (c) Sketch the graph of vand its image. y 4 -4 T (V) -2 4 -2 y 4 2 -2 V 2 T (V) X -4 -4 -2 T (V) -2 y 4 2 -2 y 2 -2 T (V) 2 2
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