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2. Let A be the standard matrix of the linear transformation which rotates every vector in R² counter-clockwise through an angle of 7/3 (radians), and B be the standard matrix of the linear transformation which reflects every vector in R2 through the ₁-axis. (i) Find A and B. (ii) Find the standard matrix of the composition of these two linear transformations by applying A first and then B. (iii) Find the standard matrix of the composition of these two linear transformations by applying B first and then A.

2. Let A be the standard matrix of the linear transformation which rotates every vector in R² counter-clockwise through an angle of 7/3 (radians), and B be the standard matrix of the linear transformation which reflects every vector in R2 through the ₁-axis. (i) Find A and B. (ii) Find the standard matrix of the composition of these two linear transformations by applying A first and then B. (iii) Find the standard matrix of the composition of these two linear transformations by applying B first and then A.

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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2. Let A be the standard matrix of the linear transformation which rotates every vector in R² counter-clockwise through an angle of 7/3 (radians), and B be the standard matrix of the linear transformation which reflects every vector in R2 through the 2₁-axis. (i) Find A and B. (ii) Find the standard matrix of the composition of these two linear transformations by applying A first and then B. (iii) Find the standard matrix of the composition of these two linear transformations by applying B first and then A. 3. Consider the linear transformation T whose standard matrix is A = (i) Does T map R onto R³? Justify your answer. (ii) Is T a one-to-one mapping? Justify your answer. -4 31 1-2 24 -4 36
Transcribed Image Text:2. Let A be the standard matrix of the linear transformation which rotates every vector in R² counter-clockwise through an angle of 7/3 (radians), and B be the standard matrix of the linear transformation which reflects every vector in R2 through the 2₁-axis. (i) Find A and B. (ii) Find the standard matrix of the composition of these two linear transformations by applying A first and then B. (iii) Find the standard matrix of the composition of these two linear transformations by applying B first and then A. 3. Consider the linear transformation T whose standard matrix is A = (i) Does T map R onto R³? Justify your answer. (ii) Is T a one-to-one mapping? Justify your answer. -4 31 1-2 24 -4 36
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