Mathematics, 18.02.2020 01:01, mxhx
Let {v1,v2,v3} be a set of vectors in Rn . If u is Span {v1,v2,v3}, show that 3u is in Span {v1,v2,v3}.(Hint: since you are told that u is in the span {v1,v2,v3}, you can automatically say that there are scalars c1,c2 and c3 so that u = c1v1+c2v2+c3v3. Your goal now is to find a way to write 3u as a linear combination of {v1,v2,v3}
Answers: 2
, then u is a linear combination of v1,v2,v3, that is, there exist scalars 
such that 
. Multiply by 3 in both sides to get 
, with 
as real numbers are closed under multiplication. Therefore 3u is a linear combination of the vectors 
, that is, 
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Let {v1,v2,v3} be a set of vectors in Rn . If u is Span {v1,v2,v3}, show that 3u is in Span {v1,v2,v...
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