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

Q: An inner product (•, ·) on R³ under which the vectors 1 Vị = 1 1 , V2 = 2 satisfy (v1, v2) = 0…

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Q: of the following vector fields, the one that is conservative corresponds to: 3xy¹+x A) F(x, y, z) =…

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Q: In order for vectors and t- 3 in a vector space R3 to be linearly t+4 in depen den t what should t…

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Q: - Consider trying to solve Ar= b where 2 3 -1 (a) Find a vector b so that Ar b has no solution. (b)…

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Q: The dot product of two vectors Y1 Y2 and j = Yn in R" is defined by a · j = x11 + x2y2 + ...+ x„Yn-…

A: According to the given information, it is required to determine a vector in R3 that is perpendicular…

Q: Show that the vectors (3+ /2,1+V2) and (7, 1 +2\/2) in R² are linear!ly dependent over R but…

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

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: 3) Use the basic definition of a Cartesian tensor to show the following: (a) That for any general,…

A: Solution : Consider a rotation of the (unprimed) coordinate axes through an angle θ to give the new…

Q: a. The zero vector 0 is in ker(A) b. If x and y are in ker(A), then so is z = x + y. c. If x is in…

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Q: What is the dimension of the vector space S=abc detEM2x3(R): a=b=c=0}

A: Dimension of vector space is number of element in basis

Q: G. It Symmetric tansor anti- Symmetric tensor, that Apg is a is an then prove

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Q: Two vector fields are F = -10 ax + 20 x (y–1) ay and G = x y ax – 4 ay + z az. For the point P(2,…

A: Given vector fields are F=-10 ax +20 xy-1 ayG=2xy ax -4ay +z azPoint P =2, -3, -4

Q: Let W1 and W2 be skew-symmetric tensors with axial vectors w1 and w2 respectively. Show that…

A: To prove this identity we will use an identity. Proof of that identity is given below:…

Q: is Cartesion Tensor o& orden 2 on the for m 3 a=(3,4,1) Find - 2 %3D Tią and a. I

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: a) T: M, → R, where M, is the vector space of n by n matrices over a field, and T (A) = det(A).

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Q: prove that kronecker and Livi-civita are tensors of rank 2 and 3 and respectively?

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Q: Let U ⊂ Rn be open and f : U → Rm be differentiable at a ∈ U. Prove that for any vector ~v ∈ Rn,…

A: To Determine :-  Let be open and be differentiable at . Prove that for any vector .

Q: If |r (t)| = c (a constant), which of the following is NOT true about the vector function r(t) от ()…

A: If (r(t)|=constant, then we can take any r(t) whose modulus value is a constant. Let r(t)= sin(t)i +…

Q: Also deduce the Jacobi identity for the cross product: u × (v × w) +w × (u × v) +v × (w x u) = 0 их

A: Introduction: We know that u×v×w=vu·w-wu·v, where u, v, and w are purely imaginary.

Q: Find the divergence of each of the following vector fields. (a) div( 5xi – 5yj)= (b) div( –5yi +…

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

Q: v.(OF = (vo) - F+o(V .F (V) F+

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Q: Find || U || and d(U, V) relative to the standard inner product on M22. 6. #].v=[ -10 15 45 10 U 1…

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Q: If u and v are vectors in R^n, and if v≠0 ⃗, then u can be expressed in exactly one way in the form…

A: first draw a figure as below

Q: al of the vector î + xj along t

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Q: Which one of th e following vector fields is not con servative? A. F (x, y) = (y e*r x e*) B. F (x,…

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Q: True or false 1- The value of v→⋅(v→×w→) is always zero. 2- For any scalar c and any vectorv→, we…

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Q: 4 If r(t) =(1+t)3/2i+(1 - t)/2j + tk, t= 0 then the binormal vector B is

A: Consider the position vector,   rt=491+t32i+491-t32j+13tk,   t=0                      Orrt=491+t32,…

Q: At how many points is the vector field F(x, y, z) = (z– ,r – 2², y – x²) irrotational? Select one:…

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Q: 2. Determine the x and y components of each of the forces shown. -800 Dimensions in mm 800 N 600 424…

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Q: Calculate Vø and V?o of the scalar field: 6 = eV=²+y?+z?

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Q: 10) Find the cross product a x b and verify that it is orthogonal to both a and b. a =  j + 7k,…

A: Let's find.

Q: Find the gradient of the following scalar fields: a) F=x^2+y^2 b) V=p^3z cos2phi

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Q: If v is a vector in R", and if k is any scalar, then: (a) ||v|| 20 (h) x = 0 if and only if y = 0

A: Given: v is a vector in ℝn and k is any scalar To show that  a) v≥0 b) v=0 if and only if v=0

Q: A constant vector field F(r, y, z) = ai + bj + ck is a gradient vector field. True

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Q: The integral of vector A= 0.25p cos(q)ap +2zaz Over the bottom of cylinder specified by 1<Zs2, p = 2…

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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: is Cantesion Tensor of orden 2 on the form 3 I= 2 a=(3,4, 1) Find - 2 T.a and a. T

A: Given that, T=31124-21-10,a=341 The objective is to find aT,Ta.

Q: b) Consider the following metric: ds² = e²A(r) dt² - e²B(r) dr² — r² (d0² + sin² 0do²), with A(r)…

A: Solution :Consider the following 4D-curved spacetime metric.ds2 =…

Q: If Aj is a covariant tensor of the second order and Bi, Ci are contravariant vectors; prove that…

A: Given: Aij is a covariant tensor of 2ndorder To find: AijBiCj is an invariant tensor

Q: If A is second order tensor ,then ylgn O ihi O

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: In Rn with inner product{x, y} = xTyderive a formula for the distance between two vectorsx = (x1, .…

A: Take two vectors x and y in an inner product space x=x1,…,xn and y=y1,…,yn then x,y=xTy

Q: The dimension of the vector space P; is equal to: Select one: O 5 none of the others 4

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Q: 5. If F = A × OP, where A is a constant vector field, show that V x F = 2A 6. If R = OP,r = ||R||,…

A: The solution are next step

Q: Let W = {[x]∈ R2^ | y > or equal to 0} .             [y] (a) If u and v are vectors in W , is u + v…

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Q: 1) Verify that d/dx(fg) is a vector space over R, or explain why it is not.

A: The objective is to find whether the ddxf.g is a vector space over ℝ. Since it is known that…

Q: Please answer in complete solution The task is to identify all the values of a and b that will make…

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Q: Use the standard inner product on R" to determine if the vectors or functions are orthogonal. 2 -3 1…

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