1. Consider Let R(A) column space of A R(A) = column space of AT, 0 1210 2511 0 372 2 493-14 by N(A) = null space of A N(AT) = null space of AT. (a) By finding the linearly independent columns, express the four fundamental spaces: R(A), R(AT), N(A), and N(AT). Also find their dimensions. b₂ (b) Find all the vectors b by b₁ [Try to establish a relation in the components of b.] Using this result, decide for -2 what value of kER the system Ax=b is inconsistent where b = [Instruction: Do not solve Ax=b explicitly.] (e) Do you see any relation between the vector b for which Ax=b is consistent and N(AT)? Can you prove this relation in general? ER such that the system Ax=b is consistent.
1. Consider Let R(A) column space of A R(A) = column space of AT, 0 1210 2511 0 372 2 493-14 by N(A) = null space of A N(AT) = null space of AT. (a) By finding the linearly independent columns, express the four fundamental spaces: R(A), R(AT), N(A), and N(AT). Also find their dimensions. b₂ (b) Find all the vectors b by b₁ [Try to establish a relation in the components of b.] Using this result, decide for -2 what value of kER the system Ax=b is inconsistent where b = [Instruction: Do not solve Ax=b explicitly.] (e) Do you see any relation between the vector b for which Ax=b is consistent and N(AT)? Can you prove this relation in general? ER such that the system Ax=b is consistent.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 42CR: Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a...
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