Suppose u and v are any vectors in R³. Which of the following is not true? Ollu + vll ≤ llull + ||v|| if llull=0 then u = 0 lluvil ≤ ||ul|- ||v|| None of the above

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Q: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

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A: (a) Find u→+v→ as follows: u→+v→=-1,2,4+-3,5,2          =-1+-3,2+5,4+2          =-4,7,6

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A: year x 1951 13 1952 23 1953 21 1954 27 1955 37 1956 52 1957 34 1958 42 1959 31…

Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

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Q: Let A and B be vectors in R. Show that ||A|| = || B|| if and only if A+ B is orthogonal to Ã- B.

A: To solve the given orthogonality problem related to vector.

Q: 25. Show that |v|u + Ju|v and |v|u – |u| v are orthogonal.

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Q: onil s 2 S = {v1,V2} = 4 5 7 8. a. Explain why S is linearly independent but is not a basis for R³.…

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Q: Please choose the right answer for the statement below: Suppose V1,V2,V3,V4,V5 are five vectors in…

A: given 5 vectors in ℝ3

Q: _3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex…

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Q: Determine whether the set of vectors orthonormal, or neither. O orthogonal O neither {(√².₁. √²)( √6…

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Q: Let -3 ----------- V3 2 V1 = 6 a. How many vectors are in {V₁, V2, V3}? b. How many vectors are in…

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Q: Consider the following vectors 3 ------ What are the norms of the three vectors? Number (4 d.p.) (4…

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Q: Find vectors v and w so that v+w= (4,5,6) and v-w=(2,5,8). This is a question with____ unknown…

A: Addition of vectors

Q: 8. Consider the vectors u, and w. If 2ū= [2, -2, -6], [-1, 1, 2], and W = [-1, 1, -1] find the exact…

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Q: 3. Write ū as a sum of vectors, one in the direction of and another orthoganal to a. 18 [4] -5 [3³]

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Q: Suppose |||| = 5 and |||| = 6, and assume and y are orthogonal. Then ||-||²7

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Q: Suppose à and are arbitrary vectors in R³ such that ||a|| = 1; |||| = 4; Let c = (2a × b) — 36. Find…

A: For given conditions we have to find the angle between  vector b and vector c.

Q: 10. Let ā = (1,2) and b= (2,1). Find projz(ā). Then show that ā– projz(ā) is orthogonal to b…

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Q: Quolel X= -gi +sj -K, Y. i-2 k yo i-2 K Find X x Y

A: (1) Consider the given vectors x=-2i+3j-k and y=i-2k   We have to find x×y   Now, x×y=ijk-2   3-11 0…

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Q: 2. If A = 2a, + 0.3a, – 1.5a, and B = 10a, + 1.5a, - 7.5a,, Show that A and B are dependent vectors.

A: The solution is given as

Q: Let 7 and w be vectors in R". Prove that If |7| = |7| = | 7 + |, then |7 - wf=3|7

A: