How many Potenhally defferent tensors of ander two can be defined by faking the ouer Product of sö and T tten Contraching ? twice

Q: - 5. Consider th gonal to vector (-

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Q: Find the Ś canlat andl vector frojections of b and a. bE.

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Q: that if all the components of a tensor in one co ordinate system are zero

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Q: 6. Prove that in n-dimensional space, symmetric and skew-symmetric tensor have(n+1) and d(n-1)…

A: Given :  n-Dimensional Space            : symmetric tensor and skew- symmetric  To Prove :…

Q: Describe the additive inverse of a vector in the vector space.P4

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

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

Q: prove by vector method that diagonals of rectangle are equal in length and bisect each oth

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Q: The dimension of the vector space ii2×3 is equal to 6. Select one: True O False

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Q: If Apq is a symmetric tensor, Bpq is an anti-symmetric tensor, then prove that ApqBpq = 0

A: Given two tensors Apq & Bpq such that Apq is symmetric and Bpq is anti-symmetric. To prove that…

Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  For each vector b,…

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Q: Give two examples of infinite dimension vector spaces.

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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: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

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 App Symmetric tensor, is anti- Symmetric tensor, is an prove that Apg Bpga o then

A: Definitions: (1) Symmetric Tensor: The tensor of second order, we denote it by Apq, is said to be…

Q: If F1 and F2 are two forces simultaneously acting on anobject, the vector sum F1 + F2 is called…

A: We know, The vector sum of all of the forces acting on a body is a single force called the net force…

Q: Describe the zero vector and the additive inverse of a vector in the vector space.P8

A: The given vector space is P8 .

Q: make an example and prove it about five vectors spanning R⁴

A: Given: Five vector spanning R4  We need to form an example and prove the given statement 'Five…

Q: The usual absolute value on the real numbers is a vector norm. Select one: True False

A: solution of the given problem is below...

Q: (c) Verify all 10 axioms to show that this structure defines a vector space over the real scalars

A: Note: According to bartleby we have to answer only first three proves please upload the rest of the…

Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

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Q: wing vector fields is not con

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

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Q: Show that there are infinitely many vectors in Rwith Euclidean norm 1 whose Euclidean inner product…

A: For a vector (a,b,c) its euclidean norm is given by a2+b2+c2. Euclidean inner product of two vectors…

Q: nay construct orthogonal vectors a an V such that for each k

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

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Q: Describe the zero vector and the additive inverse of a vector in the vector space.M2,3

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Q: What is the maximum of || Ar||∞ if ||r||∞ = 1? What is the maximum of ||Ar||2 if |-|2 = 1? For…

A: A=2123 (a) We know that Ax∞≤max∑ka1k,∑ka1k,…∑ka1k when x∞=1. Ax∞≤max2+1,2+3=5 The maximum of Ax∞ is…

Q: д(х, у) Find the Jacobian of the Ə(u, v)

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Q: Suppose we have n> 1 vectors in R" vector space where the ith element of the ith vector (for 1 ≤ i…

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Q: 18 as a linear combination of = 8 Express the vector i and j =

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Q: Show that ℝ2 is a vector space with usual addition and multiplication.

A: To prove that R2 is vector space we have to prove following; 1. R2 is abelian group under addition.…

Q: Give two examples of finite dimension vector spaces.

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Q: Show that there are infinitely many vectors in R with Euclidean norm 1 whose Euclidean inner product…

A: Dear students you have asked multiple questions. As per our policy your first question will be…

Q: Suppose V={v1,v2,...,vn} is a set of nonzero vectors, and let                    x= a1v1 + a2v2…

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Q: Define Vector addition.

A: For the addition of two vectors, we can use the parallelogram law.  The Sum of two sides equals the…

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: Give example on the inner product and same time is normed space

A: To find an example on the inner product and normed space. Definitions: Inner product space: Let V be…

Q: Show that any antisymmetric tensor can be made equal to C by suitable choice of the fixed vector a.

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Q: Suppose there is a collection of three or more two- dimensional vectors. Provide an argument…

A: Collection of two dimensional vectors mean those vector having i and j components.

Q: If A is second order tensor, then

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

Q: Show that there are infinitely many vectors in R'with Euclidean norm 1 whose Euclidean inner product…

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

Q: If æ is a fixed vector, verify that a second-order tensor C can be defined by setting C(y) = x x y.…

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Q: Show that there are infinitely many vectors in R with Euclidean norm 1 whose Euclidean inner product…

A: To prove that there are infinitely many vectors in ℝ3 with Euclidean norm 1 and its Euclidean inner…

Q: Find a vector b such that compab = 2. If a = ⟨3,0,−1⟩

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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: The dimension of the vector space of M, is 25. Select one: O True O False

A: Given that: Dimensions of the vector space of M5 is 25.

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.

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.