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(b) Consider the linear operator on R³ defined by performing the following operations in order: an expansion in the z-direction by a factor of 2, • a reflection in the x-z plane, and, • a rotation about the y-axis by an angle of T /3. Calculate the standard matrix of this linear transformation.

(b) Consider the linear operator on R³ defined by performing the following operations in order: an expansion in the z-direction by a factor of 2, • a reflection in the x-z plane, and, • a rotation about the y-axis by an angle of T /3. Calculate the standard matrix of this linear transformation.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 8AEXP
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(b) Consider the linear operator on R³ defined by performing the following operations in order: • an expansion in the z-direction by a factor of 2, • a reflection in the x z plane, and, - • a rotation about the y-axis by an angle of 1/3. Calculate the standard matrix of this linear transformation.
Transcribed Image Text:(b) Consider the linear operator on R³ defined by performing the following operations in order: • an expansion in the z-direction by a factor of 2, • a reflection in the x z plane, and, - • a rotation about the y-axis by an angle of 1/3. Calculate the standard matrix of this linear transformation.
Problem 4. (a) Define a linear operator on R² by performing the following operations in order: • a shear in the y-direction by a factor of 2, • a reflection in the x-axis, and, • a compression in the y-direction by a factor of ;. Compute the standard matrix of this operator and sketch the image of the standard unit square with vertices (0, 0), (0, 1), (1,0) and (1,1) under this linear map.
Transcribed Image Text:Problem 4. (a) Define a linear operator on R² by performing the following operations in order: • a shear in the y-direction by a factor of 2, • a reflection in the x-axis, and, • a compression in the y-direction by a factor of ;. Compute the standard matrix of this operator and sketch the image of the standard unit square with vertices (0, 0), (0, 1), (1,0) and (1,1) under this linear map.
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