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A is an m x n matrix. Check the true statements below: A. The column space of A is the range of the mapping z Ar. B. The null space of A is the solution set of the equation Ax = 0. C. The null space of an m xn matrix is in R". D. ColA is the set of all vectors that can be written as Aa for some r. %3D E. The kernel of a linear transformation is a vector space. F. If the equation Az = b is consistent, then ColA is R". %3D

A is an m x n matrix. Check the true statements below: A. The column space of A is the range of the mapping z Ar. B. The null space of A is the solution set of the equation Ax = 0. C. The null space of an m xn matrix is in R". D. ColA is the set of all vectors that can be written as Aa for some r. %3D E. The kernel of a linear transformation is a vector space. F. If the equation Az = b is consistent, then ColA is R". %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A is an m xn matrix. Check the true statements below: A. The column space of A is the range of the mapping z → Aa. B. The null space of A is the solution set of the equation Az = 0. C. The null space of an m x n matrix is in R". %3D D. ColA is the set of all vectors that can be written as Aa for some z. E. The kernel of a linear transformation is a vector space. F. If the equation Ar = bis consistent, then ColA is R".
Transcribed Image Text:A is an m xn matrix. Check the true statements below: A. The column space of A is the range of the mapping z → Aa. B. The null space of A is the solution set of the equation Az = 0. C. The null space of an m x n matrix is in R". %3D D. ColA is the set of all vectors that can be written as Aa for some z. E. The kernel of a linear transformation is a vector space. F. If the equation Ar = bis consistent, then ColA is R".
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