1. Which of the following vectors is not a linear combination of and 3 1) |3)| [:] [:] 2) '4) 5) all of them

Q: 4. For what value of a is the set of vectors {(1, 1, 1), (2, a, 2), (1, 5, 2)} linearly dependent ?…

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Q: 7. A(2,–3) and B(5, 1) are two points in R². Determine the following: a) AB b) |AB| c) a unit vector…

A: We can solve this as follows:

Q: Suppose and are non-zero, parallel vectors. Which of the following could not possibly be true?

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Q: Q2.7 You have been given the following statements. Which of them are always in R? TherC uiay be more…

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Q: 1. Using the vectors u = [4, -3] 3 = [7, 1] and w = [-5, 3], evaluate the following, if possible. If…

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Q: 6. Write DÉ as a linear combination of the vectors i and j a) D (9,-6) E (-7, 2) first write in…

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Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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Q: -0-0-0-0 3 and b (a) Determine if bis a linear combination of a,, a, and a,. (b) Determine if the…

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Q: Definition Example Given a set {x₁,..., xk} of vectors in R", we let the contained span (or c-span)…

A: Given: The given details are, Suppose the u , v are non-parallel, non-zero vectors in ℝ2. To show…

Q: ) Let 1 3 2 -2 1 -2 2 8 6. be given vectors in R³. Determine if b is a linear combination of v1, v2…

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Q: 5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendic through the points A(1, 2, 5),…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: 2. Let a, b and c be vectors in R". Prove that (a) a and (a c)b - (a - b)c are perpendicular; a b…

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Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: 2. Let a, b, c, and d be algebraic vectors in R3, For parts (a) and (b) below, state which theorems…

A: The dot product of the two vectors A→ and B→ is given by the following: A→·B→=||A→||·||B→||·cos θ…

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: 5. Given three vectors , U V and W u+2v+w=0_and_u•v=3. If ||ū||=||||=2, find . such that

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Q: Which of the following is a necessary condition for a set of vectors {V1, V2, ..., Vp} in R" to be…

A: Given that the set of vectors v1, v2,...,vp in ℝn. We have to find the necessary condition for the…

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: Example 3: For the given two vectors v and w find v+w, v-w, 3v, w-2v? 38 20.1 35-4) V+w= V-w= 3v=3…

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

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Q: 2. Let x and y be vectors in R³. Prove that y=(|x +ỷ1² − |x|² − |ÿ1²): a) Using a geometric…

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Q: 1. Let u and v be vectors in R". Suppose ||u||2 = 2, ||v||² = 1, and u·v = 1. Compute

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Q: This exercise illustrates how vector arithmetic can be used to prove propositions in plane geometry.…

A: (a) Here, u=v=u+v=1. ⇒u2=v2=u+v2=u+v·u+v ⇒(u+v)·u+v=1⇒u·u+2u·v+v·v=1⇒u2+2uvcos(θ)+v2=1⇒1+2…