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

Q: Inside Rn , suppose dimension (V) + dimension (W) > n. Show that some nonzero vector is in both V…

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

A: According to the given information,

Q: b) Prove that if b e R" is any vector, then b . X +b.a.

A: I have given the proof by using only definition of convergence of sequence

Q: The curd of the vector funchion v = Jx i+ Jgj+ ZK is ☺ xi+ yj+ zK

A: It is given that, v→=x i^+y j^+z k^   According to curl, the swirl of a vector around a point. It is…

Q: Let y= and u= 3 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.

A: Describe y as the sum of vertices x1 in span u and x2 orthogonal to u         x1=α9, 3=9α, 3α and…

Q: what are the examples of contravarient and covariant tensors?

A: Example of Covariant tensor: A'i=aijAj

Q: A. If x and y are orthonormal vectors, then find the valne of x+ yl? - |x-yl

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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: (a) Using Gaussian elimination, find a vector v such that

A: As per our guideline is multiple questions are posted we are supposed to answer only the first one.…

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 vector A-xyzi+3x'yj+ (xz-y'z) k.

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Q: If F1 and F2 are two forces acting on an object, the vector sum F1 + F2 is called the_______ force.

A: A resultant force is the single force which represents the vector sum of two or more forces. If F1…

Q: If A and B are vector fields, prove the following: V (A · B) = (B - V) A + (A · V) B+B× (V×A)+A ×…

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Q: a. A. vector.orthogenal.tr.Uxv.and.Txw.

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Q: (и, из) for Find the coordinate vector of w relative to the basis S R². Let ui (5, –4), u2 = (3, 7),…

A: Solvig by au+bv=w

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector - [';" - a 1 - ] a P = b

A: From the given information, P=1-aab1-b Let, stable vector as, w=xy

Q: Find the coordinate vector of w relative to the basis S = (u1, u2) for R?. Let ui = (5, –3), u2 =…

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Q: Find a vector B such that F = V × B and V · B = 0, where F %3D (x + Зу, у — 2z, х - 2z).

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Q: Truo or Fase ? If A is second order tensor ,then

A: The objective is to state whether the statement is true or false. If A is second order tensor, then…

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A: If F1 and F2 are two forces simultaneously acting on an object, the vector sum F1+F2 is called the…

Q: find the sum of vector AB and CD where A (1,-1) B (2,0) C(-,3) D(-2,2)

A: Let A (1,-1) B (2,0) C(-1,3) D(-2,2) be the given vector. Of course here in the problem   "-1"is…

Q: Let U be a vector space and u, v, w be three lincarly independent vectors in U. Is there a linear…

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Q: If the components of a contravariant tensor in x' coordinate system are (8,4). Show tha its…

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Q: Repeat Exercise 27 for the forces KX = (2, – 3) and KY = (- 2, 3).

A: The given two force vectors are, KX→=2,-3KY→=-2,3 When we find the addition of two vectors, then the…

Q: Ex: Show that if v, u, w are any vectors, then (H.W.) ux (v x w) + v x (w x u) +w x (u x v) = 0.

A: Dot Product Property :- a.b = b.a = a*b*cosθ

Q: Find the coordinate vector of w relative to the basis S= = (u1, u2) for R. Let u = (2, –3), u2 = (3,…

A: Given

Q: If T is a mixed tensor, then T} + T{ is generally not a tensor a tensor May or may not

A: Answer : may or may not  Hence, Option (iii) is true.

Q: Prove that a·a= = |a|2, where a is a vector with n components

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Q: 4. Let u o, where o is the zero vector. Show that there are exactly two unit vectors that is…

A: This is a problem of vector algebra.

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: 2. Let i= and (a) Compute the length of the vector u.

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Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

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Q: Find the unit vectoru in the di rection of the vector v=4 (2, 1, 2). 1 u = u = В. 1 12 u = 1 u = 15…

A: v=4(2,1,2)v=(4*2,4*1,4*2)v=(8,4,8)Magnitude of vector|v|=(8)2+(4)2+(8)2=64+16+64=144=12unit vector u…

Q: If X and Y are linearly independent vectors in R", then {0,X,Y} is linearly independent.

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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: 2 If a and b are vector functions and T a second-order tensor function of position, show the…

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Q: Is Vector Y in the Column space of A? What is the solution set? Write y as an appropriate linear…

A: the vector y is in the column space of A is the system Ax=y is consistent 819-59-13108abc=123…

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of 1 - a а P = 1 - b [ W =

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Q: If A is second order tensor, then

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

Q: A set of vectors S={v in a vector space is called linearly independent if the vector equation c…

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Q: In differential geometry give me example of covariant tensor and contra variant tensor.

A: Concept:

Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…

Q: Define and give three examples of contravariant and covariant tensors ?

A: The space of real numbers can be defined with dimensions Rn. The properties in this space can be…

Q: 4) Show that, in general, (A.B)" = B".AT How is (A.B) related to (B.A) when both tensors A and B are…

A: 4.

Q: prove that 1 Ə div A; = {√g grk Ak} = div A¹, Əx* where A; and Ai are the covariant and…

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Q: 10. The vectorj^3E is the same as vector O j^4E O j^5E O j^2E O jE

A: Solve by vector product