Three vectors v1, v2 and v3 are given (see attachment).
1. show that v1, v2 and v3 are orthonormal
2. vector w is given (see attachment). Find <w,v1> , <w,v2> and <w,v3>
3. Is w a linear combination of v1, v2 and v3? If yes, what is the combination? If not, why not?
4. is the given vector u (see attacment) a linear combination of v1, v2 and v3? Justify your answer.
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The solution ...
The 6 pages solution discusees the concepts of orthonormality and inner product. It shows how to decompose a vector into a linear combination of basis vectors.