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Math 330 Quiz 4.6 March 27,2009
Give explanations to your answers for each of the following:
1.
If
A
is an
8
×
3
matrix whose Null space has dimension 1, then what is the dimension of the
row space of
A
? What is the dimension of the column space of
A
?
SOLUTION:
The dimension of the row space and the dimension of the column space (i.e. the rank of
A
)
are the same. This is equal to the number of columns of
A
minus the dimension of the Null
space i.e. 3

1 = 2.
2.
If
A
is an
8
×
3
matrix whose Null space has dimension 1, then when we row reduce
A
to
reduced Echelon form, how many zero rows will we get?
(Does this depend on other features of
A
? If so, how?)
SOLUTION:
In reduced Echelon form, the nonzero rows of
A
will form a basis for the row space of
A
.
Since this has dimension 2, there will be just two nonzero rows. Since
A
has 8 rows, we will
get 8

2 = 6 rows which are all zero.
3.
If
A
is a
16
×
33
matrix, then what is the largest possible dimension for Col
A
?
SOLUTION:
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This note was uploaded on 09/19/2009 for the course MATH 330 taught by Professor Johnson,j during the Spring '08 term at Nevada.
 Spring '08
 Johnson,J
 Math, Linear Algebra, Algebra

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