(Left nullspace) Add the extra column b and reduce A to echelon form: [1 2 3 bi = [Ab] 4 5 6 b₂ - 7 8 9 b3 2 3 0-3-6 b₁ b₂-4b₁ b3-2b2+b 0 0 0 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?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 14E
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(Left nullspace) Add the extra column b and reduce A to echelon form:
[1 2 3
[Ab] 4 5 6
bi
1
b₂
→
2 3
0-3 -6
7 8 9 b3
0
00
bi
b2-4b₁
b3 - 2b2 + 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 [Ab] 4 5 6 bi 1 b₂ → 2 3 0-3 -6 7 8 9 b3 0 00 bi b2-4b₁ b3 - 2b2 + 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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