Find (u, v), ||u||, ||v||, and d(u, v) for the given inner product defined on R". u = (5, 0), v = (-2, –4), (u, v) = 3u1V1 + uzv2 (a) (u, v) (b) ||u|| (c) ||v|| (d) d(u, v)

Q: Determine if the function defines an inner product on R2, where u = (U₁, U₂) and v= (v₁, v₂).…

A: Define a a function on R² by  ⟨ u , v ⟩ = 8u1v1+u2v1+u1v2+8u2v2 .   Now  Symmetric. ⟨ u , v ⟩ =…

Q: Find ||u|, |v||, and ||u + v||. U= (-2,-1, 0, 1), v = (0, 1, 2, 4) (a) ||u|| (b) ||v|| (c) ||u + v||

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Q: Let (u, v) be the inner product on R² generated by A = [ 6 -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find <u, v>

Q: Find (u, v), ||u||, ||v||, and d(u, v) for the given inner product defined on Rn. U= (0, -3), v =…

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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: Let ((u,,u2,U3),(V1,V2,V3))= 2u, V1 + 3u2V2+ U3V3 be an inner product on R. Determine ||(1, – 1, -…

A: Explanation of the answer is as follows

Q: (a) Use determinants to compute the area of the parallel- ogram spanned by the vectors (2, 3) and…

A: Note the results : Suppose we have two vectors u=<u1,u2> and v=<v1,v2> .Then area of…

Q: State why (u,v) =u,³v,² +u₂³v₂² is not an inner product for u = (u,,u,) and v= (v₁,v₂) in R².

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Q: Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (1, 1, 1), v =…

A: Our guidelines we are supposed to answer only three subpart. Kindly repost other subpart as the next…

Q: The two open disks B((1,2);2) and B((-2,1);1) has intersection. True or False

A: The two open disks B1,2: 2 and B-2,1: 1 We have to find there is any intersection between these…

Q: 3. (а) Consider the vectors ū = i – 6j + 4k, ở = 2i – 5j – 3k and w = 6i – 2j + 3k Show that ū x (T…

A: Use the formula for determining the cross product of two vectors  Substitute the values given and…

Q: 6 -3 1 Let (u, v) be the inner product on R generated by A = -1 and let u = (4, 3), v= (-5,3). Find…

A: Given that   <u,v> be the inner product on ℝ2 generated by A=61-1-3. And    u=(4,3), v=(-5,3).…

Q: Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (3, 0, 1), v =…

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Q: 6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find the .

Q: Verify that the operation {x, y} = x1y1 − x1y2 − x2y1 + 3x2y2 where x = (x1, x2) and y = (y1, y2) is…

A: Given : The operation on ℝ2 is defined as  x, y = x1y1 - x1y2 - x2y1 + 3x2y2 ,  where x = (x1 , x2)…

Q: Question 7. Determine, which of the following are inner products on R?. Justify your answer. 1) (u,…

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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 ||u|| = 2, ||v|| = 3, (u, v) = 2+i. Compute ||u+v||², ||u-v||², (u + v,u - iv), (u + 3iv, 4iu).

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Q: Consider the inner product on R2 defined by ((x, x2), (y, y2)) = x11 + 4x2y2. Which of the following…

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Q: State why (u, v) is not an inner product for u = (ui, u:) and v = (v, V2) in R? %3D (u, v) = (u,v;)²…

A: We are given that u,v=u1v12+u2v22 for u=u1,u2 and v=v1,v2 in R2. We know that an inner product must…

Q: True or False: (p, q) = pq defines an inner product on P(R).

A:

Q: Use the inner product (u, v) = u,V1 2u2V2 to find (u, v). + u = (6i, -i) and v = (i, 7i) (u, v) =

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Q: Let u=-3i+3j+2k and v=i+j+3k and find u . v, that is, the cross product of u and v

A: Let  u→ and v→ be the two vectors .   i.e, u→=u1i^ +u2j^+u3k^  and  v→=v1i^+v2j^ +v3k^ Dot product…

Q: Let ((uz,u2,U3),(V1,V2,V))= 2U1V1 + 3u2V2+ U3V3 be an inner product on R, Determine d(1, – 1, –…

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Q: Use the definition of a Taylor/Maclaurin series to: a) Find the first four nonzero terms of the…

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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 ((u1,u2,U3),(V1.V2,V3))=2u1 V1 + 3U2V2+ U3V3 be an inner product on R3. Determine ((1, – 1, –…

A: Given problem is :

Q: Explain why is not an inner product for u =(u1, u2) and v =(v1, v2) in R2 when = u1u2 + v1v2 using…

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Q: Using the inner product (,): P₂ (R) × P₂ (R) → R, (p, q) = p(0)q(0) + p(1)q(1) + p(2)q(2) calculate…

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Q: For (a, B) E R?, define a function (-, -) : R² × R? → R by setting arr' + xy + Yx' + Byy' . 1. Find…

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Q: Let W(s, t) = F(u(s, t), v(s, t)) where u(1,0) = -2, u, (1, 0) = 8, ut(1,0) = -4 v(1,0) = -3, v.…

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Q: 7. Let V={(x,y) x,y € R}. Suppose addition and scalar multiplication are defined using the following…

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Q: C) Use the properties of deterrainates without expanding prove that a b C a+2x b+ 2y c+2y=0 X y Z

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Q: Suppose that c is the line segment from (a, b) to (c,d). (a) Show that [rd |x dy – y dx = ad – bc…

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Q: What is the Cartesian Product of Z × X × Y, where X = {3,–1}, Y = {m, l, 0} and Z {w,b}.

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Q: Show that each of the following are not inner products on R³,

A: (a)We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and…