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Question 2: The linear transformation R : R* + R* is the rotation about the vector (0 1 oj" with the angle according to the right hand rule. The linear transformation 3 S : R' + R is a reflection of the plane x – y + z = 0. Let T = So R. a) Determine the standard matrix for T. b) Determine the null space for T. What dimension does it have? Explain. c) Determine the Image space for T. What dimension does it have? Explain.

Question 2: The linear transformation R : R* + R* is the rotation about the vector (0 1 oj" with the angle according to the right hand rule. The linear transformation 3 S : R' + R is a reflection of the plane x – y + z = 0. Let T = So R. a) Determine the standard matrix for T. b) Determine the null space for T. What dimension does it have? Explain. c) Determine the Image space for T. What dimension does it have? Explain.

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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Question 2: The linear transformation R : R* → R* is the rotation about the vector 10 1 of with the angle - according to the right hand rule. The linear transformation 3 S : R³ H R is a reflection of the plane x – y + z = 0. Let T' = So R. a) Determine the standard matrix for T. b) Determine the null space for T. What dimension does it have? Explain. c) Determine the Image space for T. What dimension does it have? Explain.
Transcribed Image Text:Question 2: The linear transformation R : R* → R* is the rotation about the vector 10 1 of with the angle - according to the right hand rule. The linear transformation 3 S : R³ H R is a reflection of the plane x – y + z = 0. Let T' = So R. a) Determine the standard matrix for T. b) Determine the null space for T. What dimension does it have? Explain. c) Determine the Image space for T. What dimension does it have? Explain.
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