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(Left nullspace) Add the extra column b and reduce A to echelon form: 1 2 3 b₁ 1 2 3 b₁ [A b] = 4 5 6 b2 → 0-3-6 b2-4b1 789 63 0 00 b3 - 252 + b₁ A combination of the rows of A has produced the zero row. What combination is it? (Look at b3 - 262 + b₁ on the right side.) Which vectors are in the nullspace of AT and which vectors are in the nullspace of A?

(Left nullspace) Add the extra column b and reduce A to echelon form: 1 2 3 b₁ 1 2 3 b₁ [A b] = 4 5 6 b2 → 0-3-6 b2-4b1 789 63 0 00 b3 - 252 + b₁ A combination of the rows of A has produced the zero row. What combination is it? (Look at b3 - 262 + b₁ on the right side.) Which vectors are in the nullspace of AT and which vectors are in the nullspace of A?

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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(Left nullspace) Add the extra column b and reduce A to echelon form: 1 2 3 b₁ 1 2 3 b₁ [A b] = 4 5 6 b2 → 0-3-6 b2-4b1 789 63 0 00 b3 - 252 + b₁ A combination of the rows of A has produced the zero row. What combination is it? (Look at b3 -2b2 + b₁ on the right side.) Which vectors are in the nullspace of AT and which vectors are in the nullspace of A?
Transcribed Image Text:(Left nullspace) Add the extra column b and reduce A to echelon form: 1 2 3 b₁ 1 2 3 b₁ [A b] = 4 5 6 b2 → 0-3-6 b2-4b1 789 63 0 00 b3 - 252 + b₁ A combination of the rows of A has produced the zero row. What combination is it? (Look at b3 -2b2 + b₁ on the right side.) Which vectors are in the nullspace of AT and which vectors are in the nullspace of A?
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