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Homework 9, due
Friday November 4th
, in class
1.
Suppose
x
1
,
x
2
, and
x
3
are linearly independent vectors in
R
n
. Deﬁne
y
1
=
x
1
+
x
2
,
y
2
=
x
2
+
x
3
,
y
3
=
x
3
+
x
1
.
Are
y
1
,
y
2
, and
y
3
linearly independent? Prove your answer.
2a.
Are the vectors
v
1
=
±
2
1
²
,
v
2
=
±
5
3
²
,
v
3
=
±
7

3
²
linearly independent?
2b.
Write
v
3
as a linear combination of
v
1
and
v
2
.
3.
Find the coordinates of the vector
3
2
5
with respect to the ordered basis
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Unformatted text preview: 1 1 1 , 1 2 2 , 2 3 4 . 4. Let A be the matrix 1 32 1 2 1 6 2 3 4 8 11 . 4a. Find a basis for the null space of A . 4b. Find a basis for the row space of A . 4c. Find a basis for the column space of A . 1...
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This note was uploaded on 12/07/2011 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.
 Fall '08
 Zhang
 Vectors

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