Let w= (-1,4,15), v = (1, 2, 8), v = (3, 0,1). Does w belong to span(v,,v,)? If yes, then write the first vector as a linear combination of the other two.

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

A:

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

A:

Q: Find the vectors u and v whose initial point is u: (3, 2),v: (1, 4) and terminal points is (5, 6) ,…

A: Initial point is (3,2) and the ending point is (5,6) so the vector is u=(5,6)-(3,2)=(2,4)   Initial…

Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

A:

Q: Determine whether the vectors (4, 2, 3)T , (2, 3, 1)T , and (2,−5, 3)T are linearly dependent.

A:

Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

A:

Q: a) If possible, express w as a linear combination of vectors u and v. w = - (1,0, —7), и %3D…

A:

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

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Let V = {ü, v, w} where й 3 ( — 3, 2, — 3), ў — (3, 5, – 5). - Find ũ that would make a DEPENDENT…

A:

Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: Find the unit vector represented by the directed line segment with initial point A (-2,1,1) and…

A: The vectorAB = B-A=(2,-3,4) -  (-2,1,1) = (4,-4,3) So the unit vector is :…

Q: Determine whether the set of vectors is linearly independent: {(1,0,1), (3,4,-3), (2,2,-1)}.

A:

Q: The line that passes through the points (4, –2,0) and (1, 1, 1) is parallel to which vector? Check…

A:

Q: Consider the vectors [2, 1,0,0], [3, 1,0,0], [0,0,0, 1] in R'. Find a vector v so that v, [2, 1,0,…

A: We know four vectors v1 , v2 , v3 and v4 in ℝ4  will be linearly independent iff , av1→ + bv2→ +…

Q: Find the vector v whose initial and terminal points are given below. (5.4, 2.4), (0.4, –2.6)

A:

Q: If u,v and w are linearly independent vectors other than zero vector, are the vectors u, v ,…

A: No, Not Necessarily.

Q: Express the vector (-1,5, –6) in R³as a linear combination of (2,0,7), (2,4,5) and (2, –12,13).

A: Solved below

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: Find projection of vector (0, 1, 0) into the line spanned by (0, 1,0) 0(-1,0, 2) 0(-1,3, 2) O (0, 3,…

A:

Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

A: a) Given:     w=1,1,5, v1=7,7,7      v2=2,5,3, v3=4,1,-1 w=i^+j^+5k^, v1=7i^+7j^+7k^…

Q: Find a vector that is orthogonal to (−1, 2, 2)

A: Find a vector that is orthogonal to (−1, 2, 2)

Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

Q: Consider the vectors (2, 1,0, 0), [3, 1,0, 0], [0,0, 0, 1] in R". Find a vector v so that v,…

A:

Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Determine if the vectors are linearly independent or not

A: The vectors are linearly independent.

Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

A:

Q: Find the (a) component form and (b) length of the vector with initial point P(-3, 4, 1) and terminal…

A:

Q: Find the length of the vector.v = (5, −3, −4)

A:

Q: Show that the vectors (1, 1, 1), (1, 2, 3) and (3, 3, 4) are linearly independent?

A:

Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

A:

Q: Let å = (- 5, 5, – 3) and b = (4, – 1, 0). Find a unit vector which is orthogonal to å and b and has…

A: Given query is to find the unit vector orthogonal to a and b

Q: Find the length of the vector.v = (2, 0, −5, 5)

A:

Q: Find the length of the vector. v - (9, 12)

A:

Q: If the vector v has initial point P, what is its terminal point? v = (0, 0, 3), P(0, 3, -3) (x, y,…

A: Let's find.

Q: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: Show that the vector a= (2, – 5, 3) in V, (R) can not be expressed combination of the vectors a, =…

A:

Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

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: Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)

A:

Q: Find a vector which is orthogonal to the vectors ū = (2, –2, 1) and ū = (4, 3, – 1).

A: Explanation of the answer is as follows

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

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below