a Let W ER a + b+ c = 0 Prove that W is a subspace of R Find a basis for W and state the dimension of W.

Q: (2) Find a basis for the subspace W = {(a +c, 2a – b, 3a – 26 – c,b+ 2c) | a, b, c € R} of R.

A: We need to find the basis for the given subspace:

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Q: Let {u1, u2,..., Un} be an orthonormal basis for a subspace S of an inner product space V, and let p…

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Q: 5. Let W be the set of all vectors p(t) in P, such that p(0) = 0. Show that W is a subspace of P,…

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Q: The set B=(v= (1,1,1),u=(0,0, - 3),w=(2,2,0)) IS: OA Linearly independent in R3. OBa subspaces of R.…

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Q: 2) Let W be a subspace of V = Rª with basis 1 1 1 V,ミ V3 1 Using Gram Schmidt process, find the…

A: The vector of the sub-space are,

Q: {{::] a Let W = : a, b, c, d in R is a subspace of the vector space M23. Find a basis for W. c d 0…

A: Given that W=a0bcd0:a,b,c,d∈R is a subspace of the vector space M23. We have to find the basis for W…

Q: 2. Let H be the set of all vectors of the form (a – 3b, b – a, a, b) where a and b are arbitrary…

A: Let V be a vector space. H is said to be a subspace of V. If  H is a subset of V. H is closed with…

Q: 1. Let V = (Z7)4, and let W = {(a, 2a, a + 2b, b + c)|a, b, c E Z7} |(a) Show that W is a subspace…

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Q: 5. Let W be the set of all vectors p(t) in P2 such that p(0) = 0. Show that W is a subspace of P,…

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Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: Consider the subspace H of the vector space P2 given by H = {a + bt + ct² | a + 2b + 3c = 0} Find a…

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Q: Let -1 2 4 and let W the subspace of R spanned by i and v. Find a basis of W-, the orthogonal…

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Q: Let W be the subspace spanned by the given vectors. Find a basis for W-. 1 -1 1 W1 W2 -5 -2 1

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Q: Find an orthogonal basis for the subspace H of IR that is spanned by the vectors 1 1 1 -2 1 V1 = V2…

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Q: 1. Let V = (Z7)4, and let W = {(a, 2a, a + 2b, b + c)|a, b, c E Z7} (a) Show that W is a subspace of…

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Q: Let V be the vector space of 2 × 2 matrices over the real field R. Find a basis and dimension of the…

A: Let us consider the vector space V; the set B is the basis of vector space V if  B is linearly…

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Q: Let W {(a, b, c, d)| a – 5 b = 0 } be a subspace of R*. Then a basis for W is

A: The given subspace of R4 is W={ ( a , b  ,c , d ) | a - 5 b = 0 } Let x=( a, b , c , d ) be in W…

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Q: 0-0- Let ui = u2 = and set W = {w e Rª : w · v1 = w · v2 = 0}. W is a subspace of R4. Find a basis…

A: Find the dimension first and find vectors which satisfies given two relation

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A: In this question, the given set W is defined as W=abc ∈R3 s.t. a+b+c>0, for all a,b, c in R}  To…

Q: 10. Let W be the subspace of the real vector space V =R* spanned by a = (1,–1,2), 3 = (2, 3. –6), 7…

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Q: Let V be the subspace of ℝ4 spanned by the columns of the matrix  A=[1 2 3 −2 3 8 5 1 −3 −3 −4 −5 ]…

A: (a)Consider the given matrix, the columns of which spanned V:

Q: 2. Consider the set of matrices W : b : а,b€ R a (a) Show that W is a subspace of M22. (b) Find a…

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Q: Let H span {(-11,0, –5), (–3,0, –1), (–2,0, –1)}. A basis for the subspace H C R³ is { vector

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Q: Let W be the subspace spanned by the given vectors. Find a basis for W⊥

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Q: Let 3 u= and let W the subspace of Rª spanned by ū and v. Find a basis of W+, the orthogonal…

A: Given vectors, u→=-3-10-2-2,v→=132-3 The objective is to find the basis of W⊥ the orthogonal…

Q: (a) Let U be the subspace of C de fined by U = {(z1, z2, z3, Z4, Z5) E C° : 6z1 = 22 and z3+2z4+3z5…

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Q: Let W = {A € M3x3(R) : A" = -A}. (a) Prove that W is a subspace of V = M3×3(R). (b) Construct a…

A: According to the given information, Let W be defined as:

Q: 3. Consider the vectors 1 W1 E W2 = and the subspace W = span{w₁, W2, W3} CR¹. (a) Find an…

A: Given, as a matrix: 10-1121011000    ~       10-1022000000   Rank = number of pivot elements =2w1,…

Q: Let 3 -7 ,V = u -3 -3 4 and let W the subspace of R* spanned by u and v. Find a basis of w', the…

A: The given vectors are u=3-73-3, v=-12-34 and W be the subspace of R4 spanned by u and v.

Q: 2. Show that {1,x – 1, x (x + 1)} is a basis of the space of polynomials P2 (IR) and that W = {p(x)…

A: If the elements of the set are linearly independent then the set is a basis set. If Wvis a subspace,…

Q: Let W = {(a, b, c, d) E R*| a – b = 0,2b + c = d}. i. Show that W is a subspace of R*. ii. Find a…

A: We will prove the following result.

Q: Let 3 -13 3 3 and let W the subspace of IR spanned by ū and v. Find a basis of W, the orthogonal…

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Q: 5. Let S = {x + 1,x2 – 2, x – 1,3}. Find a basis for the subspace W that is spanned by S.

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Q: 2 Let A = | -4 2 Define U = {M E M2x2 such that MA = 0}. Prove that U is a subspace of M2x2. Find a…

A: We will find out the required solution.

Q: 1. Let W be the subspace of R' spanned by wi = (1, –1,0,5) and w2 = its orthogonal complement W1.…

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Q: 1. Let V = (Z;)ª, and let W = {(a, 2a, a + 2b, b + c)|a, b, c € Z7} |(a) Show that W is a subspace…

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Q: Let U={p E p2 : p(2)=0}.Show that U is a subspace of p2 and find a basis for U.

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Q: Find a basis for the subspace {p(=) e P: p(2) = -p(-2) } of P. W = A basis for W is {x² -Ex: 1 :,…

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Q: Let 9. 2 H = span 10 A basis for the subspace H C R* is { }. vector

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Q: Let H be the set of all vectors of the form (a – 3b, b - a, a, b) where a and b are arbitrary…

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Q: Let H span {(-13, –1, -3),{-9,2, –2), (-1, –5, 0)}. A basis for the subspace H C R³ is { }. vector…

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Q: 5. Let W be the set of all vectors p(t) in P such that p(0) = 0. Show that W is a subspace of P and…

A: W be the set of all vectors p(t) in P2 such that p(0)=0.