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Vector Span problem?

Show that (10, 9, 8) lies in the vector space Span{(−1, 3, 1), (4, 1, 2)}.

1 Answer
Jul 7, 2018

Answer:

Please see the Explanation for a Proof.

Explanation:

In order to show that #vecw=(10,9,8) in SP{vecu,vecv},#

#vecu=(-1,3,1), and, vecv=(4,1,2)#, we must show that

#EE a,b in RR, s.t., vecw=avecu+bvecv#.

#:. (10,9,8)=a(-1,3,1)+b(4,1,2), i.e.,#

#:. -a+4b=10...(1), 3a+b=9...(2), &, a+2b=8...(3)#.

Solving #(1) and (3), b=3, &, a=2#.

This also satisfy #(2)#.

Thus, we have, #vecw=2vecu+3vecv#.

# rArr vecw=(10,9,8) in Sp{(-1,3,1),(4,1,2)}#.