10. Let n > 2 be an integer and let V be the subset of F" consisting of vectors (x1,..., xn) satisfying X1 + x2 +...+ xn = 0, x1 + 2x2 +...+ nxn = 0. The dimension of V is (a) 2 (b) п — 2 (с) п — 1 (d) п (е) п +1

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Find u. v, uu, ||u||², (u - v)v, and u . u = , V = (a) (b) u. V u . u (c) || u ||2 (e) (d) (u. v)v…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 5. Express u = (-4, 3, —2) using the unit vectors.

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Q: 5. Determine which sets of vectors are orthogonal. (a) 1 ↑ 1 0 -5 2 1 5 -309 (b) -4 2

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Q: Suppose that u, v, and w are vectors such that cu, V) = 3, cv, w> = – 4, cu, wɔ = 7, ||u||= 1 ||v||=…

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Q: the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V, + 5v), v =…

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Q: Let a and b be vectors in R" such that ||a||=|| b||=2 and (a,b)= — . Then ||a - b||= ...

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Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: Let a and b be vectors in R" such that ||a||=||||= 2 and <a,b)=3. Then ||a-b||= ..

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Q: 14. Find a vector perpendicular to both of the vectors * (ũ + v) and (ũ – v) where ủ = 2i – j + k,…

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Q: V2, V1 + v2, 2v1 - v2 ), v = (9, 9), w = (-3/2, 2, -8) (a) the image of v (b) the preimage of w (If…

A: This is a problem of vector calculus.

Q: (2) Determine if the vectors are linear independent or linear dependent. Justify your answer. (a)…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, Vị + V2,…

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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: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

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Q: 11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors…

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Q: Let j TE 2 --- = 1 and u = = Write y as the sum of two orthogonal vectors, #₁ in Span{u} and 2…

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Q: et u and v be vectors in R 3 such that ∥u∥ = 30 and ∥v∥ = 5. What can we best say about |u · v|? (a)…

A: One must verify a few claims, using the rule of dot product.

Q: Use the function to find the image of v and the preimage of w. T(V1, V2) = V2, V1 + V2, 2v, - v2 2…

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Q: Let ~u = ( 1, -1, 0) and ~v = ( -1, 0, 1). Find ~u - ~v and ~u + ~v. b) Are the vectors ~u − ~v and…

A: Orthogonal vectors

Q: Find the best approximation to z by vectors of the form C₁V₁ + C₂ V₂ 2 5 4 -2 Z= 0- 0 2 2 2 0 V₂ -4…

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Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Let A and B be vectors in R" and let c be a real number. Then (1) ||A|| 2 0, and || A|| = 0 if and…

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Q: →→→ Let x, y, z be vectors such that x X X y x z →→ = a; y x ➜>> Z X X y = b and ° {(+5) x = -(-+)}…

A: It is given that x→=y→=z→=2 x→,y→,z→  makes angle of 600 with each other.x→×y→×z→=a →  ; y→×z→×x→=b→…

Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 V1, V1 + V2,…

A: Let us consider the transformation T: V→W defined as T(v)=w where v is preimage of w  and w is an…