## Let Bold u comma Bold v comma Bold w 1 comma Bold w 2 comma and Bold w 3 be vectors in Bold Upper R Superscript n. If u and v can both be wr

Question

Let Bold u comma Bold v comma Bold w 1 comma Bold w 2 comma and Bold w 3 be vectors in Bold Upper R Superscript n. If u and v can both be written as linear combinations of Bold w 1 comma Bold w 2 comma and Bold w 3, show that u+v can also be written as a linear combination of Bold w 1 comma Bold w 2 comma and Bold w 3.

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Math
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2022-01-03T06:46:25+00:00
2022-01-03T06:46:25+00:00 1 Answer
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## Answers ( )

Answer:Step-by-step explanation:given that

U, Vare two vectors in R^nThese two vectors can be written as a linear combination of 3 vectors

w1, w2,andw3To prove that

U+Valso can be written as a linear combination of these three vectors.Since U is a linear combination we can write for not all a,b, c equal to 0

Similarly for d,e,f not all equal to 0

Adding these we have

Here all a+d, b+e or c+f cannot be simultaneously 0.

So we get U+V can be written as a linear combination of w1, w2 w3 as follows:

Proved