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Given that the matrices A and B are row equivalent (we obtained matrix B from matrix A via Gaussian elimination), and 3 -3 9 1 -1 3 A=-1 1 -3 - and B=0 -3 3 0 0 1 5 00 (a) Find a basis for the row space of A. (b) Find a basis for the column space of A. (c) What is the rank of A? Explain your answer. (d) What is the dimension of the nullspace of A (the nullity of A)? Explain your answer.

Given that the matrices A and B are row equivalent (we obtained matrix B from matrix A via Gaussian elimination), and 3 -3 9 1 -1 3 A=-1 1 -3 - and B=0 -3 3 0 0 1 5 00 (a) Find a basis for the row space of A. (b) Find a basis for the column space of A. (c) What is the rank of A? Explain your answer. (d) What is the dimension of the nullspace of A (the nullity of A)? Explain your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given that the matrices A and B are row equivalent (we obtained matrix B from matrix A via Gaussian elimination), and 3 -3 9 1 -3 -3 3 -8 A = -1 1 3 4 and B = 0 -1 0 0 3 1 0 (a) Find a basis for the row space of A. (b) Find a basis for the column space of A. (c) What is the rank of A? Explain your answer. (d) What is the dimension of the nullspace of A (the nullity of A)? Explain your answer.
Transcribed Image Text:Given that the matrices A and B are row equivalent (we obtained matrix B from matrix A via Gaussian elimination), and 3 -3 9 1 -3 -3 3 -8 A = -1 1 3 4 and B = 0 -1 0 0 3 1 0 (a) Find a basis for the row space of A. (b) Find a basis for the column space of A. (c) What is the rank of A? Explain your answer. (d) What is the dimension of the nullspace of A (the nullity of A)? Explain your answer.
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