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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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This note was uploaded on 02/12/2014 for the course MATH 70 taught by Professor Mcgrath during the Spring '13 term at Tufts.
 Spring '13
 MCGRATH
 Math, Linear Algebra, Algebra, Equations, Vectors

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