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

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: If L and U are invertible, then (LU) – Find A from the given LU factorization: 9 -27 7-14 96 = -63…

A:

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

A:

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: An inner product on R² is defined as (u, v) = (Au) · (Av), [ 3 where A : -3 (a) Is (1, –2)…

A: Orthogonal Vectors: Two vectors x and y in an inner product space are called orthogonal, if x, y=0…

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

A:

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 A ∈ Rm×n, B ∈ Rn×r, and x, y ∈ Rn. Supposethat the product AxyTB is computed in the…

A: Let's first calculate the number of scalar additions and multiplications required for each method:…

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

A:

Q: = (3, 6) 2. It is known that u = (-2,3) and v = relative to the inner product in R? which is derived…

A: 2 Given that u=−2,3 and v=3,6 And A=2134. We have to find the u and v. We know that…

Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

A:

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

A:

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) =

A:

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

A:

Q: Q1/ Prove or disprove: A) If A is invertible and k is a nonzero scalar, then kA is invertible and…

A:

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: 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: Recall that the Euclidean scalar product in R² is defined by (x1, Y1) · (x2, Y2) := X1T2+ Y1Y2 - (i)…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

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

A:

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: Calculate the dot product of x = (3, -2, 0, 3) E R and y = (1, 2, 3, 4) ER4.

A: The dot product of two vectors x=(a1,a2,a3,a4)  and  y=(b1,b2,b3,b4)in 4th-dimensional space is: x.y…

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

A:

Q: Σα-3αβγ= (Σα) (Σα?- Σαβ) |

A:

Q: Without using determinants, show that {(2, –x,,3x²,x³} is a basis for Ps then find dimension for P3

A:

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

A: We have to find