Find the scalar product a•b when (i) a= x+2y -z and b=2x+3y +z (ii) a=x-3y +z and b=2x+y +z

Q: 9. If three planes intersect in a point then the triple scalar product (a x b) · c of their normals…

A: As per bartleby policy we are not supposed  to answer  more than one question per post. This post…

Q: Find an orthonormal basis of ℋ:  x− 2y − 3z = 0.

A: Introduction: The Gram–Schmidt process is a method for orthonormalizing a set of vectors in an inner…

Q: Compute the product 0 () 0 (²) as a 2 x 2 matrix. What kind of isometry is this product?

A: Given product is  Oπ5O2π15 where Oθ represents rotation matrix through an angle θ in anti-clockwise…

Q: Compute the flux of the vector field F(x, Y, z) = 6i + 5j + 3k through the rectangular region with…

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Q: Match the vector field with its graph. F(x, y) = yi -6+ 世 -5+

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Q: let (x,y,z) be Scalar Field and F a vector field.. $ Derive expression for D. (OF) and * (OF) in…

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Q: Find the flux of the field F =(x + y)i -(x2+y2)j outward across the triangle with vertices (1, 0),…

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Q: 9. Show that the matrix 0 0 -1 0 0 1 -1 C2 = x, x- will transform the vector y into -y

A: We have to show that the matrix C2 will transform the vector in ℝ3 into the vector -x-yz. First we…

Q: Show that LU decomposition is not possible for the matrix A, where 1 2 3 A 2 4 1 0 2

A: The given matrix is,A=123241-102

Q: (a) Find an orthonormal basis of the vector space P₂ of polynomials of degree at most 2 with respect…

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Q: Consider the scalar field f(x,y, z) = 2x² – y² + 3z? Determine V Vfl(1.-1.1) II. VxVfl1.-1.1)

A: Here, the given function is: f(x,y,z)=2x2-y2+3z2

Q: for the vector field F = 2xz i+ (1 – 4xy² ) j led by the plane z = 6 – 2x² – 2y² and the plane

A: We have to find the following conditions according to the given information

Q: Find the standard matrix of the linear operator M : R → R³ that first rotates all vectors…

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Q: Let T be an linear operator on a complex vector

A: let J=2100000002100000002000000002000000003100000003000000000100000000=[T]B Matrix J is in Jordan…

Q: Find the matrix of the orthogonal projection of R² onto ar + by 0. %3D

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Q: Let v ∈ R2 be a vector in the first quadrant. Express v in terms of its coordinate vectors with…

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Q: The inner product of anti-symmetric and symmetric tensor is а. 1 b. 0 С. -1 d. none of the above

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Q: Find the dimension of the vector space.R6

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Q: Suppose u = (5, 3,0), v = (0, 3, 9), and w = (-1, –9, –3). Compute the three triple scalar products…

A: We will solve the following.

Q: Find the standard matrix for the linear operator T: R^3 --> R^3 that first rotates a vector…

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Q: Consider the scalar field f(x,y, z) = 2x² – y² + 3z2 i. V Vfl(1.-1.1) Determine II. VxVfl1.-11)

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Q: Find the matrix A representing the reflection about the line L in R² which consists of all scalar…

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Q: Find curl F for the vector field at the point (9, -9, 5). F(x,y,z) = x²zi - 2xzj + yzk curl F =

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Q: Sketch the vector field. F(z, y) = (- 2 2 2 0 2 -2 0 -2 2 -2 2 -2 -2 2 -2 4- -4 -3 -2 -1 2 3 -2 -3-…

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Q: verify that the matrices and scalars in Exer- cise 1 satisfy the stated properties. (a) (AT)" = A…

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Q: b) Find the curl of the vector field, CurlF, if F = Ax²z²i– By:'j+Cz*k, where the coefficients A,…

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

Q: Find the level surfaces of the scalar field U = ear, where the vectors are: a = (2, 2, 1) and r = =…

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Q: ey are linearly dependent, find scalars a, b, and c, not all zero, such that au + bv + cw = 0 u =…

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Q: Sketch the vector field. y F(z, y) = (-2 | 2 -2 -2 2 -2 2 -2 -2 -2 4+ -4 -3 -2 -1 3 -1 -2- -3 -4…

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Q: Use the determinant version of the cross product to compute. u . (v X w) = (u X v) .w (the triple…

A: Let u=u1u2u3v=v1v2v3w=w1w2w3be three vectors in ℝ3.

Q: give an example of an infinite dimensional vector space V over complex numbers and a linear operator…

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Q: 2. Use matrix multiplication to find the orthogonal projection of (1, 2, - 3) onto the a. ху-plane.…

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Q: the dimension of the complexification VC thought of as a real vector space

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Q: Calculate ∇φ and ∇2φ of the scalar field: φ = e √ x^2 + y^2 + z^2

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Q: Determine a scalar r such that Ax = rx, where 1 A = and X=

A: Given, A=2112, x=11

Q: Use the quotient law for tensors to show that the array -2xy -2xz /y²+z²-x² -2yx x²+z²-y² -2yz -2zx…

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Q: Find the matrix for T relative to the basis B, and use Theorem 8.5.2 to compute the matrix for T…

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Q: Compute the standard matrix of the linear operator M : R³ → R° that first reflects all vectors about…

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

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Q: (5b) Is E invertible? How do we know? (5c) Is E diagonalizable? How do we know?

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Q: Denote three scalars A = eTE-le, B = µTE-le and C = µTE-'µ. 1. Prove that AC – B² > 0.

A: We are given three scalers A,B,C in terms of weighted matrix inner-products, and we have to prove…

Q: Show that the condition number of the square matrix, X (generated with X;j = 461-2), grows i+6j–2 as…

A: We will use the conventional definition of condition number of a matrix.

Q: Determine which set of vectors form an orthonormal. a) b) c) d) None of these 11L

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Q: Find the gradieat of the functionf = xyz-4y2z. Visualize the vector field of the gradient. %3D

A: In vector calculus, the gradient of scalar valued function denotes the direction in which the…

Q: Suppose cu =0 for some nonzero scalar c. Show that u= 0. Mention the axioms or properties you use.

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Q: Find a formula for the dimension of the vector space of symmetric n X n matrices.

A: Given: symmetric  n×nmatrix