Show that dot multiplication of vectors is positive definite; that is, show that u.u>=0 for every vector u and that u.u = 0 if and only if u = 0.

Q: Prove Ảx (B x Č) = B(Ả C) – Č(Ã B) is true by expanding Ả, B, and components (or Cartesian…

A:

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

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

A:

Q: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

A:

Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

A:

Q: Find a unit vector orthogonal to both u and v.u = (2, −1, 3) v = (1, 0, −2)

A:

Q: Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.

A:

Q: Show that if u and v are orthogonal unit vectors then u x v is also a unit vector.

A: To show: That if u and v are orthogonal unit vector, then prove that u×v is also a unit vector:…

Q: Find a unit vector orthogonal to both u and v. u = -5i – 3j - 2k | V =

A: Two vectors A and B are said to be orthogonal to each other if and only if their dot product is zero…

Q: Show that there are no vectors u and v such that 11u 11= 1, ||v|| = 2, and uxv= 3.

A: If u and v are two vectors, and the angle between these two vectors is θ Then the magnitude of the…

Q: Show that dot multiplication of vectors is positive definite; that is, show that u . u ≥ 0 for every…

A:

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

A:

Q: Determine all vectors v that are orthogonal to u.u = (0, −4, 3)

A: Given u=(0,-4, 3)we have to find all vectors v that are orthogonal to u,If u.v =0 then vectors u and…

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: Find a unit vector orthogonal to both u and v.u = (−4, 3, −2) v = (−1, 1, 0)

A: Given u→=(-4,3,-2)v→=(-1,1,0) unit vector orthogonal to both u and v is gruen by     u→×v→‖u→×v→‖

Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

A:

Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

A:

Q: A vector u for which || u || = 1 is called a(n)_______ vector.

A: u is a vector whose modulus is 1. u=1 For a vector, if the modulus or magnitude is 1 then the vector…

Q: Let nonzero vectors ū,v,weR be linearly independent. Show that there does not exist a nonzero vector…

A:

Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: Prove that if vector u is orthogonal to both vectors v and w, then u is orthogonal to v + w.

A:

Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: Let x and y be two orthogonal vectors. Then prove that +

A:

Q: Show that every plane through the origin in R3 may be identified with the null space of a vector in…

A: The null space of any matrix A consists of all the vectors B such that AB = 0 and B is not zero.It…

Q: Determine all vectors v that are orthogonal to u.u = (11, 2)

A: Now let

Q: Prove that two vectors v = (a, b) and w = (c, d) are perpendicular if and only if ac + bd = 0

A: we have to prove that the two vectors v=a,b and w=c,d are perpendicular if and only if ac+bd=0

Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

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

A:

Q: Prove that two non-zero vectors u and v in n-space are perpendicular if and only if u • v = 0

A:

Q: orthogonal to the vectors

A:

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

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: . Let x and y be two orthogonal vectors. Then prove that

A: If x is any vector then Euclidean norm or 2-norm is denoted by ||x||2 and is given by  ||x||2 =…

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: Show that if C is any two-dimensional vector then it can be written as a linear combination of the…

A: Given: C→ be any two dimensional vector spaceie.,   C→=x,y|x,y∈ℝFormula: Convex set∃ t,s∈ℝ such that…

Q: True or False Of all of the possible scalar multiples of a vector v, the orthogonal projection of u…

A: This is a result which states that " Orthogonal projection of any vector a onto b is closest to a"

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

A:

Q: If v is orthogonal to both u and w, then v is orthogonal to every vector in span{u, w} Select one: O…

A: Given:  v is orthogonal to both u and w So, v . u = 0 and v . w = 0   To find: To check if v is…

Q: 2. Prove the following identities related to the cross product of vectors (а) (и х у)хw — (u · w)v –…

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: Let u= 2 and v= 2. Show that among all the scalar multiples cv of the vector v, the projection of u…

A:

Q: Using the vectors from the previous problem, find the projection ul of v onto the vector u and find…

A: We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product…

Q: If x = (x1, x2)T , y = (y1, y2)T, and z = (z1, z2)T arearbitrary vectors in R2, prove that xTy = yTx

A: x = (x1, x2)T , y = (y1, y2)T are arbitrary vectors in R2 .

Q: ind a vector orthogonal to both u and j+k. u=2i-j+3k

A: we have been given two vectors,  u = j+k. v=2i-j+3k   the unit vector that is orthogonal to both…

Q: Let x, y, and z be vectors in Cn and let α and β becomplex scalars. Show thatz, αx + βy} = α z, x} +…

A: Given: z,αx+βy=αz,x+βz,y

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

A: