Problem 4. (a) Define a linear operator on R? 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.
Problem 4. (a) Define a linear operator on R? 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.
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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