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Consider the following matrix A: 3 -1 7 3 97 4 -4 14 10 -5 9. 3 3 4 3 7 For each of the four fundamental subspaces of A, give the dimensionality of the subspace and calculate a basis for that subspace (you may use your code from homeworks to help with this). (A) Col(A) (B) Nul(A) (C) Col(AT) (also called the "row space of A")

Consider the following matrix A: 3 -1 7 3 97 4 -4 14 10 -5 9. 3 3 4 3 7 For each of the four fundamental subspaces of A, give the dimensionality of the subspace and calculate a basis for that subspace (you may use your code from homeworks to help with this). (A) Col(A) (B) Nul(A) (C) Col(AT) (also called the "row space of A")

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.5: Iterative Methods For Computing Eigenvalues
Problem 51EQ
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Problem Four Consider the following matrix A: 3 -1 7 3 97 -4 4 -4 14 10 -5 9. 3 3 4 -2 6 6 3 7 For each of the four fundamental subspaces of A, give the dimensionality of the subspace and calculate a basis for that subspace (you may use your code from homeworks to help with this). (A) Col(A) (B) Nul(A) (C) Col(A") (also called the "row space of A") (D) Nul(A") (also called the "left null space of A") Now, again using code from homeworks or any other technique you prefer, show that (E) Nul(A") is the orthogonal complement of Col( A) (F) Nul(A) is the orthogonal complement of Col(A") Solution:
Transcribed Image Text:Problem Four Consider the following matrix A: 3 -1 7 3 97 -4 4 -4 14 10 -5 9. 3 3 4 -2 6 6 3 7 For each of the four fundamental subspaces of A, give the dimensionality of the subspace and calculate a basis for that subspace (you may use your code from homeworks to help with this). (A) Col(A) (B) Nul(A) (C) Col(A") (also called the "row space of A") (D) Nul(A") (also called the "left null space of A") Now, again using code from homeworks or any other technique you prefer, show that (E) Nul(A") is the orthogonal complement of Col( A) (F) Nul(A) is the orthogonal complement of Col(A") Solution:
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