Lecture 6 Notes

5 2 a set of two vectors example u1 let 2 1 u2 4 2

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Unformatted text preview:  2 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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