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[2 1 0 - 1 1 1 1 Determine a basis for row(A), and null(AT). What are 0 2 -1 0 ons of each, and how do they relate to the number of columns of the matr

[2 1 0 - 1 1 1 1 Determine a basis for row(A), and null(AT). What are 0 2 -1 0 ons of each, and how do they relate to the number of columns of the matr

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 38EQ
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[2 1 0 -17 1 1 1 1 Determine a basis for row(A), and null(AT). What are the 02 -1 0 dimensions of each, and how do they relate to the number of columns of the matrix? Draw a diagram, Show the details of how the transformation TA takes elements of the domain and moves them to the codomain. Label what the domain and codomain are. You must show the nullspace and indicate where it goes. You must show the span of each of the basis vectors for the range(T) and show a representative space in the domain that goes to each of the spans. How many dimensions are lost via this transformation? What do points, lines, planes, 3D-spaces, and 4D-spaces become after being transformed? Let A =
Transcribed Image Text:[2 1 0 -17 1 1 1 1 Determine a basis for row(A), and null(AT). What are the 02 -1 0 dimensions of each, and how do they relate to the number of columns of the matrix? Draw a diagram, Show the details of how the transformation TA takes elements of the domain and moves them to the codomain. Label what the domain and codomain are. You must show the nullspace and indicate where it goes. You must show the span of each of the basis vectors for the range(T) and show a representative space in the domain that goes to each of the spans. How many dimensions are lost via this transformation? What do points, lines, planes, 3D-spaces, and 4D-spaces become after being transformed? Let A =
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