Let H be the set of all vectors of the form Find a vector v in R such that H = span {v}. -s

Q: Two vectors u and v in space are if and only if u X v= 0

A: Given vectors in space are u and v The vectors cross product is u x v = |u| * |v|* sin(angle between…

Q: (a) A: va+v. (b) A: (av). (c) A: √ av.

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find a vector of matching dimension that is not in the given span. span

A:

Q: (a) Give examples of three distinct vectors v1, v2, v3 in the vector space R3 such that v2 E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

Q: Consider the set V of all vectors of the form (x y z)T where x, y and z are real numbers. 3. Show…

A:

Q: With T defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: The given matrix  and the vector  and  is defined by .The aim is to find the vector  whose image…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find all values of a such that the vectors = and are perpendicular

A: Given:The vectors are  and  are perpendicular.To Find:The value of .Concept Used:When two vectors…

Q: 2) Write the vector v as a sum of proj span{.…...} (v) and proj spo span{m} orthogonal set V₁,..., V…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find the angles between each vector in A where the set of vectors A = { [1, 1, 1], [1, 1, 0], [1, 0,…

A: Question explained below :Explanation:ANSWER :​​

Q: Is the set of (infinite number of) vectors { (0,0,c) }, where c is a real number, a vector space…

A:

Q: -2st] Let W be the set of all vectors of the form 3s + 5t t - 2s H v = Find vectors ū and 7 in R³…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given- If L is a line in 2-space or 3-space that passes through the points A and B, then the…

Q: 2s Let H be the set of all vectors of the form Find a vector v in R' such that H span {i}. -s S

A: Spanning set of H

Q: |3s + 3t Let W be the set of all vectors of the form 3s - 4t. Find vectors u and v in R³ such that…

A:

Q: be rational numbers. Show that R is a vector space over the rational numbers Q, using standard…

A: We proved all the properties of a vector space.

Q: Let v1, V2, V3 and u be vectors in R". If u is orthogonal to each of v1, V2, and v3 then u is…

A:

Q: S be the set of all vectors of the form u and v such that S = span {u, v}. 4s + 5t -5s + 5t s + 2t…

A:

Q: (i) Let {u, v} be linearly independent vectors in a vector space V. Determine whether set {v – u, v…

A: 7 (i) Given, u, v be linearly independent vectors in a vector space.

Q: Find the length of the vector v = (9, 3, 9). ||v|

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given, A=( 1,1,0 ); B=( -2,3,-4 ); P=( -3,1,6 )To find: Distance from point P to the line through A…

Q: Given any linearly independent set of vectors V = {v, V2, , }, prove that there is at least one…

A:

Q: 1 1 -1 Let S ). Determine the dimension of the span of S and which vectors can serve as a basis for…

A:

Q: 2 -7' Let j = and u .Write j as the sum of two orthogonal vectors, , in Span {u} and 2 orthogonal to…

A:

Q: Let I be the line in R³ that consists of all scalar multiples of the vector 2. Find the orthogonal…

A:

Q: B. Is C a real vector space? Explain.

A: