Let -1 2 4 and let W the subspace of R spanned by i and v. Find a basis of W-, the orthogonal complement of W in R4. ||

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:

Q: Let V = U® W and let {u̟,u2, ... , uk } be a basis for the subspace U and {W1,W2, ..., Wk } be a…

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Q: (2) Find a basis for the subspace W = {(a+c,2a – 6, 3a – 26 – c, b + 2c) | a, b, c E R} of R4

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Q: Let V be a subset of R³ consisting of all solutions to the linear system x-y-5z=0. Show that V is a…

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Q: 1. Let B = be a 1 basis for the subspace V. Find the matrix that projects any 4 vector v E R* onto…

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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: 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: Consider the vectör X1 = X2 = 4. in R3, and let W be the subspace Span{x1, X2}. (a) Find an…

A: Given :-  Consider the vectors  x1 = 2-11   , x2 = 5-44 in ℝ3. and let W be the subspace span  x1 ,…

Q: Let W be a subspace of R" given by -E- W= ER | a+b=D0 and c-d=0; a,b,c,dER. Which of the following…

A: We need to find a basis for the following.

Q: Is the set of all vectors of the formb, where a, b, and c are any real numbers with a +b+c > 0, a…

A: A subset W of Rn is a subspace of Rn if it satisfies Non-emptiness:  The zero vector is in W.…

Q: Let W be the subspace of P3 spanned by {t³ +t² – 2t + 1, t² + 1, t³ – 2t, 2t³ + 3t² – 4t + 3}. Find…

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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 W be the subspace of vectors in R3 that are orthogonal to w = (-1, 1, 1).  Find a basis for W.…

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Q: Let W be the set of all vectors = E R such that xı – 2x2 + 3r3 = 0. (Geometrically, W is a plane…

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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: 3. Let V be a subspace of R" and B:= {v1,..., V} be a basis for V. Prove that each vector in V can…

A: Explanation of the answer is as follows

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…

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

Q: a Is the set of all vectors of the formb. where a, b, and c are any real numbers with a +b+c>0, a…

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: 4) Prove that the following subsets of R4 are subspaces, and for each subspace find a basis and the…

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Q: 4. Find a basis and the dimension of the subspace W of V = M22(R) spanned by %3D -5 2 -4 A = B = C =…

A: Given:          V = M2 × 2(ℝ) spanned by A = 1-5-42 ; B = 11-15 ; C = 2-4-57 and D = 1-7-51   To…

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 = ( { (x.y,z) ER3: x+y-z 0) be a subspace. A basis of w+ is [A].

A: Solution

Q: Let W be a subspace of Rº generated by the following vectors 1 1 2 1 2 W1 W2 W3 W4 = W5 8. -2 3 8 a:…

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Q: Let M = x2 :¤1, x2 E R X1

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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 W be a subspace of Rn with an orthogonal basis {w1,..., wp}, and let {v1,..., v4} be an…

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Q: Let U be the subspace of R' defined by U = {(x1,22, 23, 74, #3) E R³ : #1 = 3x, and z3 = 774} . (a)…

A: Let U be the subspace of R5 which is defined by U=x1,x2,x3,x4,x5∈R5:x1=3x2 and x3=7x4 (a) We have to…

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: 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…

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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Q: Let Uj and U2 be vector subspaces of a vector space V over the real numbers. Suppose that V1, V2, V3…

A: We shall answer first question only as you’ve asked more than one question. For others kindly post…

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 v, = (43 2 1), v2 = (-2 0 -1 0), V3 = (0 3 0 1) a) Find the subspace of R" spanned by these…

A: The given vectors are: v1=4, 3, 2, 1, v2=-2, 0, -1, 0 and v3=0, 3, 0, 1 The subspace W spanned by…

Q: 3) Find a basis for the subspace of R that consists of the intersection of the planes X-3Y = 5Z and…

A: This is a problem of vector space.

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: 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: Let H={p € P3: p(0)=p(1)%3D0} be a subspace of P3. Show that 8 = {-2+2t, - is basis for H using…

A: Given: H={p∈ℙ3:p(0)=p(1)=0} is a subspace of ℙ3 B={-2t2+2t,t3-t} To show that B is a basis for H…

Q: 4. (a) Find a basis for the subspace H of R spanned by the following vectors: 00000 1 (b) What is…

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Q: 2. Let V = Rn and let {e1,..., en} be the standard basis for V. a) Give an example of a subspace of…

A: We will use , if S=v1,v2,....vm are vectors such…

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

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Q: Let V be the vector space of 2 × 2 matrices over the real field R. Find a basis and 5 dimension of…

A: Given A=12-13B=251-1C=51211D=34-25

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

A: Let V be a vector space over field F . Let W be a subset of V then W is said to be subspace of V…

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.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.