Math 70 sec1_3ov

Let v 1 2 1 and v 2 4 2 a find a vector in span v

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Unformatted text preview: n v 1 , v 2 . (b) Describe Span v 1 , v 2 geometrically. 11 Spanning Sets in R 3 x3 v2 v1 x2 x1 v 2 is a multiple of v 1 Span v 1 , v 2 Span v 1 Span v 2 (line through the origin) 12 x3 x2 v2 x1 v1 v 2 is not a multiple of v 1 Span v 1 , v 2 plane through the origin 4 EXAMPLE: Span v 1 , v 2 Let v 1  2 2 a line or a plane? 6 and v 2  3 . Is 3 13 1 3 Let A  EXAMPLE: 2 8 1 and b  . Is b in 3 05 the plane spanned by the columns of A? 17 Solution: 1 3 1 0 A 2 8 5 b 3 17 Do x 1 and x 2 exist so that Corresponding augmented matrix: 12 8 31 3 0 5 17 1  2 8 0 5 21 0 5 17 1  2 8 0 5 21 0 0 4 So b is not in the plane spanned by the columns of A 14...
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