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3 . a. Determine if u 1 , u 2 is a linearly dependent set or a linearly
independent set.
b. Determine if v 1 , v 2 is a linearly dependent set or a linearly
independent set.
Solution: (a) Notice that u 2 _____u 1 . Therefore
_____u 1 _____u 2 0
This means that u 1 , u 2 is a linearly ________________ set. 6 (b) Suppose
cv 1 dv 2 0.
Then v 1 v 2 if c 0. But this is impossible since v 1 is ______ a multiple of v 2 which means c _____.
Similarly, v 2 v 1 if d 0. But this is impossible since v 2 is not a multiple of v 1 and so
d 0. This means that v 1 , v 2 is a linearly _________________ set. A set of two vectors is linearly dependent if at least one
vector is a multiple of the other.
A set of two vectors is linearly independent if and only if
neither of the vectors is a multiple of the other. 7 x2
4 3 2 1 1 2 3 4 x1 linearly ___________________ 3 2 1 1 2 3 linearly ___________________ 8 3. A Set Containing the 0 Vector
Theorem 9
A set of vectors S v 1 , v 2 , , v p in R n containing the...
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 Spring '08
 KOSTROV
 Linear Algebra, Algebra, Linear Independence

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