four vectors ~v1, ~v2, ~v3 and ~v4 be given by ~v1 = (1, 0, 2), ~v2 = (0, 1, −1), ~v3 = (1, 8, −6), ~v4 = (1, 2, 0); Let the vector space V be the linear span of ~v1, ~v2, ~v3 and ~v4. (a). Find all values of k such that the vector ~u = (2, 1, k) belongs to V . Explain. a.2)Are the vectors {~v1, ~v2} linearly independent? Explain. a.3)Find the dimension and a basis of the space V .

Q: Find the unit vector in the direction of <4,2>

A:

Q: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

Q: Find the vector PP, 1. Р.(3,2) P, (5,7) 2. P(-2,-1) 3. Р (3,3) P,(4,-5) P, (5,5) 2

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: A = [-2,4,-2,-4,        2,-6,-3,1,        -3,8,2,-3,        0,2,5,3]  Find a non-zero vector R^4…

A:

Q: A = [-2,4,-2,-4,        2,-6,-3,1,        -3,8,2,-3,        0,2,5,3]   Find a non-zero vector…

A: Given matrix is A=-24-2-42-6-31-382-30253

Q: Describe the relationship between the point (10,13) and the vector

A: We have to describe the relationship between the point (10, 13)  and  vector  <10, 13>

Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

A:

Q: find the components of the vector PQ. P = (-}, 3, 1), Q = (4, 6, 0)

A: P=-12, 92, 1,  Q=4, 6, 0

Q: Suppose that u, v, and w are vectors such that cu, V) = 3, cv, w> = – 4, cu, wɔ = 7, ||u||= 1 ||v||=…

A:

Q: Find  vector z + vector y if vector z= and vector y= . graph

A:

Q: There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the…

A:

Q: The vectors (v_1=(-1,2)), (v_2=(-2,1)), and (v_3=(0,0)) are dependent. , answer as true or false…

A: The objective of the question is to determine whether the given vectors v1=(-1,2), v2=(-2,1), and…

Q: Construct a vector that is perpendicular to the plane containing (−2, 4, 1),(3, 3, -1) and (1, 0,…

A: Construct a vector that is perpendicular to the plane containing (-2,4,1),(3,3,-1) and (1,0,2)

Q: If the cross product of two nonzero vectors is the zero vector, then each of the two vectors is a…

A: Explanation of the answer is as follows

Q: Check that the space generated by the vectors (1, 3, 5), (1, 4, 3), (1, 1, 9) is equal to the space…

A:

Q: Determine whether the vectors (1,2,3), (5,6,7), (9,10,11), and (4,8, 12) are linearly independent.

A:

Q: find a vector that is orthogonal to (1,2,3) and (4,5,6). do not use cross product.

A: Let's find vector that is orthogonal to given two vectors.

Q: Determine whether or not the given vector b is in the span of the vectors u₁ and u₂. [2] = [3], b…

A:

Q: The normal vector of 2x + By - 16.7z = -8 is: ○ [2, 뮤, -16.7, 8) ① [호, 꽃, 16.7, -8] ① [올, 꽃, -16.7]…

A: We have given equation of a plane  92x+133y-16.7z=-8 Comparing this with the equation  lx+my+nz=d We…

Q: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

A: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: we will write the given vector as linear combination of vectors in as and find the unknown…

Q: Find a unit vector in the direction of

A: Given that,   vector = <6, 3, 2> = u¯ (Say)   Unit vector = u¯u = <6,3,2>62+32+22 =…

Q: In R^3, consider the three points A(2, -1, 4), B(3, 4, -2) and C(-1, 2, 7). (a) By an appropriate…

A:

Q: Find the angle between two vectors u = and v =

A:

Q: *-[1]-[1] (b) x= -09--0 (d) x = B--- =x (J),

A: (a).    x=21  ,  y=-1  1 (b).    x=    1   4-3  ,   y=513 (c).    x=   3-4   5  ,  y=-1  0  1 (.)…

Q: Express the vector b = a₁ + a2 + 2 -4 as a linear combination of the vectors a₁ = a3 = b -2 3 7 , a₂…

A: