Let W be the set of all vectors of the form W = Span{u,v}. Write the vectors in W as column vectors. 4t 4t 4s-2t 5s =S = su + tv 4t 4t 4s- 2t 5s Show that W is a subspace of R4 by finding vectors u and v such that

Q: a) Find all values of a so that polynomials f = 4t-a and g = 5t-6 are linearly dependent in P₁.…

A: We can find the value of 'a' for which the given polynomial is linear dependent.

Q: Let S be the subset of R2 consisting of all vectors of the form (a, b + 3). a) Show that (5, 2),…

A:

Q: Find vectors u and v whose initial and terminal points are given. Determine whether u and v are…

A: The u vector can be computed as: u=6-1i+11-1ju=5i+10j

Q: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z = 0 y? + 3 x = 3 z Explain…

A: The solution is given as

Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

A:

Q: Question 1 Let W be the set of all vectors of the form a) [α] b where -2a +6b-6c = 0 Lc -3 Determine…

A:

Q: Write the vector w = (1, 1, 1) as a linear combination of vectors in the set S. V2 V3 S = {(1, 2,…

A: See the attachment.

Q: Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 0 0 -4 0 1 -1 01 1 0 0

A:

Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, v2, V3) such…

A:

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

A:

Q: Show that the set is linearty dependent by finding a nontrivial inear combination of vectors in the…

A: we have to show that the set is linearly dependent by finding a nontrivial linear combination of…

Q: 3 -1 V3= 4 3 4 -2 2. 2.

A:

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: Find each vector sum u + v. a. u = (1, 4), v = (2, −2) b. u = (3, −2), v = (−3, 2) c. u = (2, 1), v…

A: a). b).

Q: V₁ = V1 V3 = V2= 4 [ 3 [-1] 2 3]

A: We use the properties of linear combination to

Q: Consider the vectors u₁ = ------- 2 and the vector : 3 B = If IS in the span of ₁, ₂, 3, 4, write…

A: The given vectors, and the vector .The aim is to find the coefficient of the linear combination of…

Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: if W is the subspace spanned for the 3 vectors, find the sets that serve as a basis for W choices:…

A: The given vectors: v1=-1-75  ,    v2=4-59 ,    v3=69-1

Q: Determine a basis for the vector space spanned by the vectors 3. V1 2 ,V2 .Vs 17 12 O A. {V1, V3,…

A:

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: Q-2: a) combination of the vectors X = (1,2,3,0) and Y = (2,1,6,0). b) a linearly independent set of…

A:

Q: 21 3 Find a basis for the subspace of R³ consisting of all vectors 22 such that 61 - 7x2 - 4x3 = 0.…

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: 1. Let v, = (43 2 1), v, = (-2 0 -1 0), v3 = (0 3 0 1) a) Find the subspace of R* spanned by these…

A:

Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: Consider the following two sets of Euclidean vectors: X U = -------- 7x²y + 2 wz=0 W X W = W…

A:

Q: 21 Find a basis for the subspace of R³ consisting of all vectors 2 such that -81 + 9x2 + 4x3 = 0 13…

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: