Let v,,v,.v be vectors. Show that at least one of the vectors can be written as a linear combinations of the others if and only if the vector equation

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: If v is a vector,then v + (-v)=.................

A: If v is a vector, then v+-v=___.

Q: If v1, v2 E R³ are linearly independent vectors and v3 ¢ span{v1, V2} then {v1, v2, v3} must be…

A: We have to check linearly independent

Q: If three vectors vị, v2, V3 E R° are linearly dependent, then one of them must be a scalar multiple…

A: GIVEN THREE VECTORS v1, v2, v3 belongs to R^3 are linearly dependent

Q: If i = (a, b, 0), ï = (a, 1, 6), and (1,1, 12) are vectors in R Determine the value of b so that and…

A:

Q: Find the constants c1 and c2, such that vector = c1 +c2

A: In this question, we have to find the value of constant c1 and c2 for the given condition  with…

Q: Show that the vectors V1 = ( 1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = ( 1, -1, -4, 0 ) and V4 = (…

A:

Q: Suppose vị and v2 are vectors with |v1| = 2, |v2l = 3, and vị · v2 = 5. Let v3 = proj,, v2, V4 =…

A:

Q: let v = (1, 3, −2) and w = (2, −1, 4). Find all the vectors orthogonal to both v and w.

A: Given: The vectors v=1,3,-2 and w=2,-1,4. To find: The vectors orthogonal to both v and w.

Q: () (3) The vectors and are Select one: a. Linearly dependent b. Linearly independent

A:

Q: Determine if the vectors are Linearly Independent or Linearly Dependent. -2 [1 -5 =|2.X2) = -3 ,x6)…

A: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns…

Q: Find all vectors v such that xv =.

A: Given: 1,2,1×v=3,1,-5 We have to find all the vectors v such that the given equation is satisfied.

Q: Let u, v, and w be linearly independent vectors. Show that (u+v), (u-v), and (u-2v+w) vectors are…

A:

Q: Which of the following vectors MUST be linearly dependent? here a,b,c,d,e,f,g,h,i,j,k & l are real…

A: The objective is to find that which of the vector must be linearly dependent It is given that…

Q: Show that the vectors v, = (0, 3, 1, -1); v =(6, 0, 5, 1); v (4, -7, 1, 3) form a linearly dependent…

A: Given vectors v1 = (0, 3, 1, -1); v2 = (6, 0, 5, 1); v3 =(4, -7, 1, 3) . Let c1. v1 + c2. v2 + c3.…

Q: Let v = -7i - 7j-3 k and w =-3i+ 4j +6 k. Then the vector v – w can be written as

A: note : vector addition or subraction can be performed as  a⇀+b→ = (ax+bx,ay+by,az+bz) similarly for…

Q: Find all values of b for which the vectors are orthogonal 〈b, 3, 2〉,〈1, b, 1〉

A: Concept - If two vectors say u and v are orthogonal, then their dot product is equals to zero.That…

Q: Show that if {V1, V2} is a linearly independent set of vectors and v3 does not lie in Span {V1, V2},…

A:

Q: If a, B, y are linearly independent vectors of V(R), show that a + B, B + y, Y +a are also linearly…

A:

Q: (a) Show that the vectors v1 = (1, 2, 3, 4). v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

A:

Q: 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0, -1] in R'. Decide whether they…

A:

Q: If k is a real number, then the vectors (1, k), (k, k + 56) are linearly independent precisely when…

A: If k is a real number, then the vectors (1, k), (k, k +56) are linearly independent precisely when k…

Q: The vectors u and v are ________ if and only if u ∙ v = 0.

A: If the dot product of two vectors is zero ,                    If and only if they are orthogonal;…

Q: Which of the following pairs of vectors are linearly independent? Ou= (1,0) and w = (0,2). Ou =…

A:

Q: ) Show that the three vectors vị = (1, 2, 3, 4), v2= (0, 1, 0, – 1), and v3 = (1, 3, 3, 3) form a…

A:

Q: When V is spanned by {v1, v2, . . . , vk} and one of these vectors can be written as a linear…

A:

Q: express each vector in the form v = y1i + y2j + y3k. 5u - v if u = <1, 1, -1>and v = <2, 0,…

A: Given vectors

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: Determine whether the vectors v, = 1 10 and 11 are linearly %3D V3 independent.

A:

Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = (9, 3), v = (-2,…

A: The given two vectors are u=9, 3 and v=-2, 6 We have to determine whether the given two vectors are…

Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: Determine if the vector 2 b = 3 5 can be written as a linear combination of the vectors V₁ = 1 and…

A:

Q: 1. Consider the vectors [2, 1,0, 2), [3, 1, 0, 1), [1, 1,0, -1) in R. Decide whether they…

A:

Q: Let a = (-1,–3, 1). Find a unit vector parallel to a having positive first coordinate 1 3 -1

A: Unit vector

Q: Determine if the vectors vị = (1, –1,3, –1), v2 = (1, –-1, 4, 2), v3 = (1, –1,5, 7) are linearly…

A: We have to determined the vectors v1=(1, -1, 3, -1), v2=(1, -1, 4, 2), v3=(1, -1, 5, 7) are linearly…

Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = (9,3), v = = (-2,…

A: We can check whether the two vectors are parallel, orthogonal or neither by definition as below.

Q:

A:

Q: (B) If ū and ỹ are two vectors then prove that ū can be written as a vector parallel to v plus a…

A: given that ,  u→ and v→ are two  vectors

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: Determine whether the vectors {(1,-1,2).(-1,1,2).(0,0,1)} span R3. If they do, give the linear…

A: To discuss the linear independence (or otherwise) of the given vectors and describe their span

Q: (a) Show that the vectors v1 = (0, 3, 1, – 1), v2 = (6, 0, 5, 1), and v3 = (4, – 7, 1, 3) form a…

A: We have to check  linear dependent

Q: })- The vectors and are Select one: a. Linearly dependent b. Linearly independent

A:

Q: Show that if u and v are linearly independent vectors, then so are  u + v and u -v.

A: Given :           u and v are linearly independent vectors.   To prove :               u + v and…

Q: If a = (3, 0, -1), find a vector b such that comp, b = 2. %3D

A:

Q: 6. Let ū, ū, and w be vectors. Explain why any linear combination of ū and ở is also a linear…

A: Consider any two vectors x→ and y→, let the linear combination of these vectors be denoted by a→,…

Q: Let a = (4, 8, -6) and b = orthogonal to a. (2, 2, –7) be vectors. Decompose the vector b into a…

A: We are given a=(4,8,-6) and b=(2,2,-7) be the two vectors. We have to decompose the vector b into a…

Q: Find all vectors u that satisfy the equation (1,1,1)×u= (−5,2,3).

A:

Q: Let

A:

Q: Prove that two vectors are linearly dependent (taken as a set of vectors) if and only if one vector…

A: Let X and Y be two vectors. Suppose these two vectors are linearly dependent. [To prove: One vector…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.