If æ is a fixed vector, verify that a second-order tensor C can be defined by setting C(y) = x x y. Find the components of C and show that it is antisymmetric. Show that any antisymmetric tensor can be made equal to C by suitable choice of the fixed vector r.

Q: Find the norm of and the unit vector ū in the direction of T if 5 3 = ||7| = 5, ||

A:

Q: What is the dimension of the vector space M,x3R)?

A: SOLUTION-

Q: If V is a vector space than show that cV=V

A:

Q: Prove that in a given vector space V, the zero vector is unique.

A: This question is related to linear algebra topic vector space.

Q: In a vector space V, prove that (-1)v= -v for all v E V.

A:

Q: 21. With A as in Exercise 17, find a nonzero vector in Nul A and a nonzero vector in Col A.

A: Given matrix is A=6-4-32-969-6 The column space of A is the space generated by the column vectors of…

Q: Suppose that the vectors {v, u, w} are linearly independent in some vector space V. Prove that the…

A: Given that the vectors u, v, w are linearly independent in some vector space V. Then the linear…

Q: If w is a vector such that w+(ŵ×ü) = v,then prove that only if u is perpendicular to v.

A:

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: Prove: If {u. ) and {W} span the same vector space, then u, are linearly dependent.

A:

Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

A:

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: Find the norm of a and the unit vector u in the direction of if 1 3 x = ||*|| = 13 = = 81 -4 Y ♡

A:

Q: Let ø = $(x), u = u(x), and T = T(x) be differentiable scalar, vector, and tensor fields, where x is…

A: According to the given information,

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

A:

Q: compute the vector v if the coordinate vector vS is given with respect to each ordered basis S for V

A: Given that, S=1-200,-1301,1000,0-110Also,vS=0102

Q: If A ism X n, prove that every vector in null(A) is orthogonal to every vector in row (A).

A: Given:  A is a m×n matrix  To prove that:  Every vector in null(A) is orthogonal to every vector in…

Q: If A(r, s, t) be a function of the coordinates in n-dimensional space such that for an arbitrary…

A: Given: Ar,s,t is a function of the coordinates in n-dimensional space such that for an arbitrary…

Q: : The dimension of the vector space Pa is equal to: Select one: 4 2 none of the others

A: Any vector in the vector space P4 is a linear combination of this set of polynomials: {1, t, t^2,…

Q: Consider a vector space that consists of the linear combinations of the following functions: {1, sin…

A: Let V={1,sinx,cosx, sin2x,cos2x,sin(2x),cos(2x),cos3x,cos(3x),sin(3x)} set of vectors v1,v2,....,vn…

Q: Determine the basis that generates the following vector space by clearing the variable y: M = {(x,…

A:

Q: For the vector space M, we define the standard inner product by the 22 formula (U,V)= tr(U'V).…

A: We find cosine of the angle between the given matrices.

Q: Find a basis for the space spanned by the given vectors, vl,., v5. 3

A:

Q: Let B and C be bases for a vector space V and let the change-of-coordinates 3 . If [v]c = 7 what is…

A: Given that B and C be bases for a vector space V and let the change of coordinates matrix from B to…

Q: snip

A: If v = &lt;a, b&gt; is an algebraic vector whose initial point is the origin, then v is called…

Q: snip

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

Q: In any vector space V, show that (a + b)(x + y) = ax + ay + bx + by for any x, y e V and any a, be…

A: In any vector space V, show that (a+b)(x+y)=ax+ay+bx+by for any x,y belong to V and any a,b belong…

Q: "If u E R' is a nonzero vector, then there exists a vector v E R° so that the matrix A = (u v) has…

A: Given statement is true.

Q: Let a E R". Prove that ||x|| = max |r;| is a vector norm by showing that it satisfies i=1,...n the…

A:

Q: Find the norm of x and the unit vector ü in the direction of x if ||| = u =

A:

Q: Find the norm of i and the unit vector i in the direction of a if ||7|| =

A: Solutions

Q: Find the coordinate vector of a -2 with respect to the basis B %3D for R.

A:

Q: Find the weighted Euclidean norm of the given vector. 10 with weights w = v = ||v|| = Ex: 1

A: Here, we need to find the weighted Euclidean norm of the vector v=102 with the weights w=111. Let…

Q: The vector v, is in Span{ v2,., Um } if and only if ( v1,., Vm ) are linearly dependent. O True O…

A:

Q: Given a vector space E, let (u)iel be a family of vectors in E. Let v EE, and assume that v = Eielu.…

A:

Q: 3. For any vectors U, V and scalars a, b, prove that (a) (aU) x (bV) = ab(U x V)

A:

Q: Show that if A is both diagomalizable and invertible, then so is A-1. Find a unit vector in the…

A:

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: are vectors in R³ are linearly independent but ü,v,w are linear dependent. Show that there exist…

A:

Q: What is the dimension of the vector space R

A: The objective is to find the dimension of the vector space R5.

Q: If aj is a symmetric covariant tensor and b, a cova- . riant vector which satisfy the relation ajjbx…

A:

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

A:

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

A:

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

A:

Q: The vector v, is in Span{ v2,., Vm } if and only if ( V Vm ) are linearly dependent. O True O False

A: Check is it dependent or not

Q: Let x, y, and z be vectors in a vector space V. Prove that if x + y = x + z then y = z.

A: if, x+y=x+z we use transportation and solve it

Q: If T and H are invertible linear operators on a vector space V(F), then show that TH is invertible…

A:

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

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.