a 2. Is the set of vectors of the form a subspace of R³? Show your proof. a+2b 3. Show that the vectors v = (0, 3, 1, -1); v = (6, 0, 5, 1); v3 = (4, -7, 1, 3) form a linearly dependent set in R? 4. Express V1 in number 3 as linear combination of V2 and V3. 5. For which value of x do the following vectors form a linearly dependent set in R V =x, x,

Q: Determine the dimensions of the following subspaces of R* a) All vectors of the form (a, b, c, d),…

A: We have to find the dimensions of vector

Q: Q6) Determine whether the set S spans R³. If the set doesn't span R³, give a geometric description…

A:

Q: Which of the following is a subspace of R3: { (a,a+2,1) : aER} { (1,b,b+1) : bER} {(a,b, 0) : a,b…

A: We will use the fact that any subspace contains the origin to find the answer

Q: Which of the following are subspaces of R^3?  W ={(x, y, z) :x+y+z=0}

A: Given, W=x,y,z:x+y+z=0 Let, 2,-1,1∈W Let, -1∈F

Q: Which of the following sets are subspaces of R' ? I. The solution set of the system Aæ = 0, for a 4…

A: The given sets are: The solution of the system Ax=0, for a 4×3 matrix A. The set of all vectors x1,…

Q: Which of the following is a subspace of R? O A. All vectors of the form (a, 0,0). O B. All vectors…

A: Subspace of a vector space:  A subset V of ℝn is said to be a subspace of ℝn if 1. The zero vector…

Q: 4. Determine whether the sets span R' for part a and R' for part b. If the set does not span R? for…

A:

Q: {[::] a b 0 Prove that W22 d 0 |,a, b, c, d e R {[: а11 а12 а13 is a subspace of M23 а11,а12, а13,…

A: According to the given information, it is required to prove that W22 is a subspace of M23.

Q: Wi = {(a,b,c,d) E R* : a+ b+ c = 0} ve W2 = = 0, b = 0}, Being subspaces of R^4 {(a,b,c,d) e Rª : a+…

A: For the given subspaces W1 and W2, we have to calculate…

Q: Q: Let W, ={(a, B.Y, 8): a=y+28, y= 28} and W2 {(a, B.Y, 8):a-y-0} be two subspaces of V,(R). Find a…

A:

Q: 13 - Which one of the followings is NOT the subspace of R? ? =O W = {(a,2a): a e R} W = {(a, a + 1):…

A:

Q: (a) Every vector of R? is a linear combination of the vectors (-2, 3), (1, 1) and (4,1)? (b) Is…

A:

Q: a a subspace of R³? Show your proof. La+2b] the set of vectors of the form

A: Given the set of vectors of the form aba+2b , which can also be expressed as:             W =…

Q: Which one of the followings is NOT the subspace of R2 ? W = {(0,–2a): a e R} - W = {(2a, a): a e R}…

A: To find which one is not a subspace.

Q: Is the set of vectors of the form [a,b,a+2b] a subspace of R^3

A: If W is a non empty subset of the vector V, then W is a subspace of V if and only if the following…

Q: -8 a) Is the set of all vectors x = u + tv, wheret ranges over all real numbers, a subspace of R3 ?…

A:

Q: Q2) Let ( Maxa ,t, ) be a linear space over R and (За 0 0 B={0 b0+(0 -b 0):a, b,c €R} be a subspace…

A: We are given: B=3a000b000c+a000-b000c; a, b, c ∈R be a subspace of M3×3 To find: dim(B)

Q: Find the distance from the point x = (1, 3, -2) of R3 to the subspace W consisting of all vectors of…

A:

Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 17, U₁ 2, U₂ = 0-16 16 24 31…

A:

Q: Find the closest point to y in the subspace W spanned by v, and v2. 11 9- -1 3. The closest point to…

A: concept:

Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y= 9 15 4 9 The closest point to…

A:

Q: Let W be the subspace spanned by u, and u₂, and write y as the sum of a vector in W and a vector…

A:

Q: S= {[a b c] eR³|a = b and c= 0} is a subspace of R. ylgn ihi

A: I have orived S is a subspace

Q: i) Determine whether or not the set w - ((x.y.2) ej+y +-1) is a subspace of w i) Write (1,7,17) as a…

A: W is not subspace because (0,0,0) does not belongs to this set  ( 0^2 + 0^2 + 0^2 is not equal to 1)…

Q: Which of the following sets is NOT a subspace of R'? {E} [1 Го 2 31 The set of solutions to the…

A: Following sets are given

Q: The set W = 3x-y= z-5w 0 is a subspace of R".What is the dimension of w Select one: а. 2 b. 4

A: easy to see

Q: c) Let us now consider the vector subspace B= Calculate the coordinates of the vector V5 =…

A:

Q: Show that w is in the subspace of R* spanned by v,. V2. and v3. where these vectors are defined as…

A: To find -

Q: Which of the following vectors is an element of the subspace W=span{(1,1,0),(0,1,1)}? (a) (2,0,-2)…

A:

Q: show what W = {(a,0,b)| a,b E R)  is a subspace of R^3

A: Given : W={(a,0,b)|a,b∈R}   To Show : W is subspace of R3

Q: Which of the following is the dimension of the subspace a W = b :a = b – c and a,b,c,d € R } c Rª ?…

A:

Q: [3] Let vi = |2|,v2 8, and w 6 Determine if w is in the subspace of R generated by v, and v2. O a.…

A: If w is linear combination of v1 and v2 then only we can say that w is in the  subspace of R3…

Q: Which of the following is a subspace of p2? O a. R2 x, e R W = Зх, + 1 1. Ob. W = ER| x*2 2 0 C. ER?…

A:

Q: Which of the following is the dimension of the subspace W = :y = x+z and x, y, z, w e R} CR ? (a) 0…

A:

Q: Determine if y is in the subspace of R4 spanned by the columns of A. -5 15 -6 -9 7 -7 -8 A = 6 13 y…

A:

Q: For every two vectors u and v in R? the subspace spanned by {u, u + v} is the same as the subspace…

A: In this question,  We find linear span of the given vectors u and v.then check the equality with the…

Q: Which of the following is a subspace of R? O A. All vectors of the form (a, 0, 0). B. All vectors of…

A: To choose correct option we will use the following theorem Theorem: A non-empty subset W of a vector…

Q: Determine the triple (rank A, dim Nul A, dim Row A) and state which of the following statements is…

A: 1. To determine the triple (rank (A), dim null A, dim row A), where the columns of the matrix A are…

Q: Let V = R? and K = R. Which of the following are subspaces of V? Give reasons for your answers.…

A:

Q: Find the dimension of the subspace U = {[x, y, z, t]|x+4y-z = 0; x-2z+ t= 0}. Select one: а. 4 b. 2…

A: Given subspace is U = {[x, y, z, t] | x+4y-z = 0;x-2z+t=0}

Q: Which of the following are subspaces of R3, if it is not explain briefly why not. (a) The zero…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 7. Let V be a 70-dimensional vector space and let W₁ and W2 be 30-dimensional subspaces. What is the…

A: Given V be an 70-dimensional vector space  W1and W2be 30-dimensional subspaces A vector space is a…

Q: Let U, Uz, U, be the following subspaces of R: U; = {(a, b,c) : a = c}, Show that (a) R = U + U2,…

A: We use definition of subspace

Q: a+b |a, b, c e R) of My? a +e 6- a каn C? b-c ,каn C What is the dimension of the subspace U kan Ç О…

A:

Q: Q3. Point a base of this subspace of R*: W = { (x,y,z,t) ||-y+z=0,t - = 0 }

A:

Q: Consider the vectors: V1 = (2,0,0,-2), |V2 = (–14 –7,–12,54). V3 = (0,1 1|-6) V4 =…

A:

Q: Find the closest point to y in the subspace W spanned by v, and v2. 1 - 2 - 1 1 2 y = V1 = 1 %3D V2…

A: The closest point to y in W is the projection of y on W.

Q: Which of the following is a subspace of R 3? O A. W={(x,y.z) € R³ | y=/2. B. S=((x,y,z) €R³ | x – y=…

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Q: Let W be the subspace of R spanned by the vectors 3 and -6 12 Find the matrix A of the orthogonal…

A:

Q: Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector…

A: