Unformatted text preview: basis for the nullspace is
. Finally, AT =
00
1
13
13
−3
T
→
so the nullspace of A has basis
. Note the orthogonality
26
00
1
between the column space of A and the nullspace of AT . And between the nullspace of A
and the rowspace of .
A
10
For B =
the ﬁrst column forms a basis for the column space and the rows are
30
1
visibly dependent so the vector
is a basis for the column space and (1, 0) is a basis for
3
10
the row space. The row reduced echelon form of B is
so a basis for the nullspace
00
0
13
T
is
. F...
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 Fall '05
 HUI
 Math, Linear Algebra, Algebra

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