Prove that for any vectors u, v, w , the set span{u+v,u – v, 3u – 3v + 2w} contains u, v, and w . (You must show this in general, without assuming the vectors u, v, w have any particular values or any specific dimension.)

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Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) = 1, (u, w) = 6, (v,…

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A: The objective is to prove the above expressions.

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A: The solution is:

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A: See solution below

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Use the values given above for substitution after simplifying the problem.

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A: u and v are vectors.

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Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) = 1, (u, w) = 5, (v,…

A: According to question,Given data,u, v = 1,u, w = 5,v, w = 0,u=1,v=3w=4

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A: Let u=u1, u2, u3  ,  v=v1, v2, v3  &amp;  w=w1, w2, w3 be the vectors. Now, v+w=v1, v2, v3+w1, w2,…

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A: The given vector is v = 3, 3

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Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) = 1, (u, w) = 6, (v,…

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Q: Suppose that u, v, and w are vectors in an inner product space such that (u, v) = 1, (u, w) = 5, (v,…

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