3. Let A = (-1 2 and B = 2 0 I. Compute tensor products A®B and B® A: II. Compute Hadamard products Ao B and Bo A: III. Compute A'•B and (A® B)`':

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: 4. If ij,k are mutually perpendicular unit vectors and u is an arbitrary vector, prove that (i-u)(i…

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Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

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

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Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

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A:

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

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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: (×q) × (gxv) + (gxg) x (xv) + (x) x (qxv)

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Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

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A: Given u→=-1,0,7v→=8,-4,0

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Q: If vectors b, c and d are not coplanc then prove that vector

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Q: If ū = 2î – î and w = î + 2ĵ, find the compo- nent form of V = ũ + w and sketch the specified vector…

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Q: 16. Let F = 2a, - 6a, = 10a- and G = a, + G,a, + 5a;. If F and G have the same unit vector, G, is…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: By using vector scalar multiplication and vector triple product, prove the identity below: Ã x [Ã x…

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Q: If it is known that the internal product of the vectors ā (4, x, -2) and ƃ (1, x + 1,5) is 6,…

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Q: Does A(u x v) = Auxv +ux Av?

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Q: Let a = (5, 4) and b = (5, – 8). Compute the dot product. a b

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Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: 1. Consider the Cartesian tensors i) ii) Or Or.) (a) Identify their orders. (b) Rewrite them in…

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Q: Let a and b be vectors in R" such that ||a||=||||= 2 and <a,b)=3. Then ||a-b||= ..

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Q: r- {{: :] T = " E M22| a = - dis a vector space under standard matrix addition and scalar…

A: I have proved T is a subspace

Q: Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.)…

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

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Q: 4. a) b) Let x = 27 + 3j - k, y = i- j + 4k and Z = −3ỉ + ]. Express the vector x – ỷ – 3ž in terms…

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A: Vector: - The term vector comes from the Latin word vector, which means "carrier." Vectors transport…

Q: (-9,6) Use matrices to reflect the vector the line y = x. ove

A: Topic:- algebra

Q: 2. Consider the vectors =(1,2,3,0),= (0,1,2,3) and = (2,3,4,-3) Let = (1,1,1,1) (a) Is a linear…

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Q: 3. Demonstrate the following relationships involving the determinate (a) Vector cross product (b)…

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Q: 16. For any vectors a, b and c, show that a. (axb) xc lies in the plane of a and b b. (a x b) X c =…

A: Step 1: Reference: Vector Calculus, Vector triple product

Q: Let a and b be vectors in R?. (a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain…

A: Given: a,b∈ℝ2 If a=a1,a2 and b=b1,b2 then areaa,b=a1b2-a2b1. To do: Express the area2b+5a,b-2a in…