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: 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: Use the inner product (p, q) = aobo + azb1 + azb2 to find (p, a), ||P||, |||, and d(p, q) for the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

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

Q: а. v(Ã ·) = Ã × (V x B) + B x (v x Ä) + (Ã ·v)Ē + (B · V)Ā b. · (Ã × B) = B · (v × Ã) – Ã · (V × B)…

A: Part(a): ∇A⇀·B⇀=A⇀×∇×B⇀+B⇀×∇×A⇀+A⇀·∇B⇀+B⇀·∇A⇀ From the left-hand side of the given equation,…

Q: Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), ||p||, ||9||, and d(p, q) for the…

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Q: Let n:Z→ 2 the n(Z) =: %3D {3Z,1+3Z,2+3Z} {3Z,1+3Z} {3Z}

A: Let π:Z→Z3Z To find  : πZ

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: Use the inner product (p, q) = abo + a,b, + a,b, to find (p, q), ||p ||, ||9||, and d(p, q) for the…

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Q: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (1, −2, 2, 0), v = (2, −1, 0, 2)

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Q: The domain of f(x) = V x2 + x – 6 | is : a) ]-4, 1[ b) ]-00, 4[U]1, +0[ c) ]-00,-3[U]2, +00이 d) ]-3,…

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Q: ) Differentiate: Y(u) = (u-2+u-³)(u³ + 3u?) и и

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Q: Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), ||pl|, |la||, and d(p, q) for the…

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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: n(U)=85, n(A)=43, n(A∩B)=22, n(C)=12, n((A∪B)′)=24, and (A∪B)∩C=∅. Find the following. (1) n(C′)=…

A: Given , n(U) = 85 ,  n(A) = 43 n(A∩B) = 22 ,  n(C) = 24 n((A∪B)')=24 n((A∪B)∩C)=∅

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: Use the inner product (o, 9) = 2obo +a1b1 +a2b2 to find o, 9), |P||- |||, and d(p, a) for the…

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Q: Use the inner product (p, q) = aobo + a¡b1 + azb2 to find (p, q), ||P||, ||g||, and d(p, q) for the…

A: Given polynomials are: p(x) = 3 - x + 2x^2 q(x) = x - x^2 We know that the inner product is given…

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

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Q: 3. Differentiate. a) M(u) (1- 4u²)(u+2) b) g(x) = (-x+ 3)(x-10)

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Q: Let W (w1, w2, w3) = UxV (cross product) such that U(-3, 3, -3) and V(1, 1, 7) %3D find w2 Answer:

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Q: S 22² +2+1 dz, where с Z² +4 b) Compute i) ( = {Z : 121=1} ii) C = {z: 17-i |=2} 17 (iii) C = {z :…

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