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Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 26EQ
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A12: Probiem 12 Previous Problem Problem List Next Problem The figure below shows where a linear transformation f maps the three standard basis vectors from its domain. The grids in the figures are unit grids. Vectors with their tip on the grid are in the xy-plane, while vectors with their tip not on integer-coordinate points the grid are not in the xy-plane. eg e1 |f(e3) a. f : R* → R" for k = and n = b. The set of vectors { e1, e2, ez} is (select all that apply): A. a basis for the codomain B. a basis for the domain C. linearly independent D. a spanning set c. The set of vectors { f(e1), f(e2), f(e3) } is (select all that apply): A. a spanning set |B. a basis for the domain C. a basis for the codomain P. inearly independent
Transcribed Image Text:A12: Probiem 12 Previous Problem Problem List Next Problem The figure below shows where a linear transformation f maps the three standard basis vectors from its domain. The grids in the figures are unit grids. Vectors with their tip on the grid are in the xy-plane, while vectors with their tip not on integer-coordinate points the grid are not in the xy-plane. eg e1 |f(e3) a. f : R* → R" for k = and n = b. The set of vectors { e1, e2, ez} is (select all that apply): A. a basis for the codomain B. a basis for the domain C. linearly independent D. a spanning set c. The set of vectors { f(e1), f(e2), f(e3) } is (select all that apply): A. a spanning set |B. a basis for the domain C. a basis for the codomain P. inearly independent
d. The linear transformation f is (select all that apply): A. onto B. one-to-one C. both onto and one-to-one e. Find the matrix for the linear transformation f (relative to the standard basis in the domain and codomain). That is, find the matrix 1 A such that f(x) = Ax. For instance, enter [[1,2], [3,4]] for the matrix 3 4
Transcribed Image Text:d. The linear transformation f is (select all that apply): A. onto B. one-to-one C. both onto and one-to-one e. Find the matrix for the linear transformation f (relative to the standard basis in the domain and codomain). That is, find the matrix 1 A such that f(x) = Ax. For instance, enter [[1,2], [3,4]] for the matrix 3 4
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