Find (u, v), ||u||, ||||, and d(u, v) for the given inner product defined on R". u = (-8, 15), v = (5, –12), (u, v) = u· v (a) (u, v) (b) ||u|| (c) ||비|| (d) d(u, v)

Q: 6. Find UV (dot a) Ū · V = (2, 3, -

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Q: Find u, u = (-1, 4), v = (4, 5) (a) ||u|| v, uv, and d(u, v). (b) ||v|| (c) (d) U V d(u, v)

A: The given vectors u=-1, 4, v=4, 5. We have to find the values of u, v, u.v, du, v.

Q: u = 3i – 2 j+4k v=i-3j-k 18) (Section 9.7) Find the cross product in space i j KI 3 -2 4 -3 -1|

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Q: If u xv=uxw and u ‡ ♂, then u = w.

A: The given statement is: If u×v=u×w and u≠0→, then u=w

Q: 42. Rather than use the standard definitions of addition and scalar multiplication in R®, let these…

A: The given question can be solved as shown in step2.

Q: 1: Let u = (-3,2, 4) and v = (2, -4,6). a) Find u o (v), b) Find u x v. c) Find Proj,u.

A: Here given that                        u=(-3, 2, 4)                and  v=(2, -4, 6)

Q: Given the vector (x <- c(5, 2, 7), what would x^2 return? O [1] 78 O [1] 196 O [1] 25 4 49 O [1] 10…

A: Given that, the vector is        ,we need to find .

Q: Find each dot product and using properties of the Dot product 1) (3, 4 ) * (2 , -3) 2) (-3, -5) * (1…

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Q: If u=(2,4)�=(2,4)  and v=(3,−4)�=(3,−4)  then proju(v)≈

A: The objective of this question is to find the projection of vector v onto vector u. The projection…

Q: If u=(1,4)�=(1,4)  and v=(3,2)�=(3,2)  then proju(v)≈

A: The objective of this question is to find the projection of vector v onto vector u. The projection…

Q: 9. Let A=span{v = (-1,–1,2), i = Projau. (2,3,0)} and w (1,2, 3). Find

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Q: Find the norm of the projection of u onto a ( || proj,u || ) with the following: (a) u=(1, – 2). a…

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Q: True or False: (p, q) = p(1)q(1)+p(2)q(2) +p(3)q(3) defines an inner product on P2(R).

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Q: 7. Let u = (2,1, −1) and v = (√√2, 1, 1). Find the decomposition of u into vectors that are parallel…

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Q: 6. Show that each of the following are not inner products on R³, (a) (u, v) = U₁V₁ + U2V2; (b) (u,…

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Q: Let a = (3, −4, 9) (a) Find k such that b = (−2, k, −6) is parallel to a. (b) Find k such that b =…

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Q: 18) (Section 9.7) Find the cross product in space u = 3i – 2 j+4k v=i-3j-k

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Q: Find Imf and Kerf of the following linear maps: a) f(x₁, x₂ + x3) = (x₁ - x₂ + 2x₂) x₁ + x3, x₁ + x₂…

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Q: Let u= (1, 1, 4, 5), v = (1,4, -4,9) and w = (3, 1, 2, 3). Evaluate: a) dx2 dx3dx4(u, v, w) = b)…

A: Step 1: Step 2:

Q: Suppose that û, VER" with llû)) = 3 11111= √5 and ū. V =-3, Find the following 1. (3ù + V). (ū - 41)

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