Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (1, 1, 1), v = (2, 3, 2), (u, v) = u1v1 + 4u2V2 + U3V3 (a) (u, v) (b) ||u|| (c) ||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: 7 Given the inner product space (R³(R),+,·,· ), where xoy = 3x₁y₁ + 2(x₂Y₁ + X₁Y₂) + 3x₂Y/₂ + 2x3V3,…

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Q: In Question, compute the indicated quantity using the specified inner product.

A: Given: a0+a1x+a2x2,b0+b1x+b2x2=a0b0+a1b1+a2b2 Using the identity v=v,v. 1+x+x2=1+x+x2,1+x+x2…

Q: 2. Let (X,(x) and (Y, (,)) be Hilbert spaces. For (x1,y1), (2, y2) = X x Y, put ((x1,y1), (2, 2))xxy…

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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: 3. Let z = (21, 22), w = (w₁, W₂) E C². Show that (z, w) = z₁w₁ + Z₂W₂ is an inner product on C²

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

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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: 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: Let u = (−3, 2), v = (3, −2) and A = - [ i]. 1 4 NOTE: Give exact answers. | (a) Find ||u|| relative…

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Q: . Show that (x, y) = 4x1y1 – 7x2y2 for vectors x = (x1, x2) and y = (y1 y2) in R2 defines an inner…

A: Given two vectors x and y in R2. We need to show that the given function in x and y defines an inner…

Q: Let r = (2,-i, 1), and y = (-i, 3,1 + i) be vectors in C3. Compute (x, y), ||x||, |ly|l, and…

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Q: Let S = { (0,0), (0,3), (1,0), (1,2), (2,0), (3,2) } Find S', the transitive closure of S

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Q: Find (u, v), ||u||, ||v||, and d(u, v) for the given inner product defined on R". u = (5, 0), v =…

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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: 8) Suppose A E Mnxn(F) is diagonalizable. Let A1,· , Ak be the (distinct) eigenvalues of A. a) Prove…

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

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Q: 9) Suppose u, v € V, where V is an inner product space, and ||u|| = ||v|| = 1 and (u, v) = 1. Find u…

A: I have used the property of norm,  IIxII=0 off x=0

Q: 2 In C, (x, y) = xAy* is an inner product, where A = i ). Compute (x, y) -i 3 for r = (1+ i, 3i) and…

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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…

Q: Problem 2. Let U = {a+bx+ca²+dr³ € P3 (R): a-b+d=0}, 2(i) Find a finite subset S of P3 (R) such that…

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