Let (u, v) be the inner product on R² generated by A = [ 6 -1 and let u = (3, −5), v = (7,4). Find (u, v). (u, v) = = 12] ₁ -2

Q: Find u v, uu, |v||2, (u v)v, and u. (3v). . u = 8i + j - 3k, v = i - 4j + 3k (a) u. V (b) u. U (c)…

A: This question is related to vectors, we will solve it using given information.

Q: Find u v, uu, ||u||2, (u v)v, and u. (2v). . u = 5i + j - 9k, v=i4j + 5k (a) (b) u. V u u (c) ||u||²

A: According to Bartleby's guide line we only do first three parts of multi-part questions.Given,

Q: Find the conjugate of z = u+w If u = 6+2i,z= 1+4i

A: Step 1: The conjugate of a complex number z=a+bi is: zˉ=a−bi i.e., it is obtained by changing the…

Q: Calculate the scalar triple product u (vx w), where u = . (Use symbolic notation and fractions where…

A: Here we have to evaluate the scalar triple product u. (v x w) .

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: By evaluating the determinants, verify the addition rule for the 2 x 2 case: a12 a22 la21 a22 la21…

A: Determinate

Q: Determine the values of x, y and z if (x+y+z)i + (y-z+1)j + (x-z)k=0. (x−y)i + (y+2z)j +…

A: A vector  is equal to the  vector if all the individual components are equal to

Q: (4) Use determinant to find the area of the triangle with vertices (0, 0), (x1,Yı), and (x2, Y2) in…

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Q: 2. Let B = {v₁ =, √₂ =, V3 =, V4 =}. Use determinant to determine whether B is linearly independent…

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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: (c) Determine the values of a and b if T(x,y,z) = (2x+y+z,a+3y,b+4z) is not self- adjoint.

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Q: Suppose that u × v = ⟨1,0,4⟩. Find (2u−3v) × v.

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Q: Compute u x v. (a) u = 2i + 3j+ 4k, v = -i+ 3j – k (b) u =i+ k, v = 2i + 3j – k (c) u =i-j+ 2k, v =…

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

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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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: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (2, 1, 1), v = (3, 2, −1)

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Q: 2. Using a = (a₁, a2, a3), b = (b₁,b₂, b3), = (C₁, C₂, C3) and k as scalar, prove all properties of…

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Q: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (1, 4), v = (2, 1)

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: Integrate: Show that B(p+1,q)+B(p,q+1)=B(p,q).

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Q: Find curl (2z i + 3x j+ 2y k). curl (2z i + 3x j+ 2y k) = )i + ( i )j + ( i i )k

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Q: Find V. (F × G), if F(x, y, z) = 5xi +j+ 7yk and G(x, y, z) = xi+yj – zk. - V. (F × G) =

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Q: Consider, 21u = 2x – 3y and 21v = -–x+y Find the value of the Jacobian a (x, y) a (u, v)

A: 21 u = 2x - 3y, 21 v = -x + y

Q: |(u+ v) x (u – v)I = 2|u x v|

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Q: valuate a.j8 1 b.- ¡7

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

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: Alsan tet A = and B = 15 [4 101 l7 15J 3 (a) [ Let c 3. Find cA. (b) ts] Find A + B (c) Find the |A|…

A: use property of matrix.

Q: 3. Find all real numbers t for V = (20 t,4t - 4,5t², t²) are orthogonal. - which = (1,5t,-4t, t³)…

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Q: Assume that (U)=110, n(B′)=55, n(A∩B′)=25, and n(A∩B)=27. Find n(A∪B)

A: For any two events A and B, it is known that n(A or B) = n(A)  + n(B) – n(A ∩ B).

Q: Need c) only use product rule 3. Differentiate. a) M(u) = (1– 4u²)(u+2) b) g(x)= (-x+ 3)(x- 10) c)…

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Q: Suppose u = (4, 1, 1) and v = (–4, −1, −3). Then: u + v= Ա υ V= u= 2u= -1/v= 7u - 6v=

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