4 Let the basis for W is -5 -1 then the orthonormal basis for W is 3 а) 1 3/2 1 3/2 1 b) 3/2 3/2 3 c) 1 1 3 d) -5 3/2 1 3/2

Q: 2) Show that S ER° defined by S = {(1,0, 5), (0, 2, -1)} is linearly independent. Extend S to be a…

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Q: 2 Let A = -3 -1 %3D 1 Find an orthonormal basis of the image of A.

A: Consider the matrix: A=22-3-117 Let v1=(2,-3,1) v2=v2-v2.v1v1.v1v1 =(2,-1,7) -…

Q: snip

A: The basis in n-dimensional space is called the ordered system of  linearly independent vectors. Let…

Q: If A = {v1, v2, ..., vn} be a basis for FV and n ≥ 2 then, is B = {v1+v2, , v2+v3, ..., vn+v1} also…

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Q: Let 4= [ -1 1 2 4 -2 2 Find an orthonormal basis of the row space of A.

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Q: 4. Prove that ū = (1,0, 1), ở = (2, 2, –1) and w = (-2,3,0) are a basis for R. Use these three…

A: Given u=(1, 0,1), v=(2, 2,-1), w=(-2, 3,0)  To check they form a basis for R3 or not.

Q: 4. A basis for R3 is Use Gram-Schmidt to find an orthogonal basis for the space.

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Q: (2) Find an orthonormal basis of ColA, where 3 -5 1 1 1 1 A = -1 -2 3 -7 8.

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Q: Let W= span{(1,2,-1,0),(2,2,0,1),(1,1,-1,0)}. Use Gram Schmidt to find an orthogonal basis for W.

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Q: Find a basis for the null space of matrix A. A = 1 2 Basis is

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Q: Let A = 3.6 1 -8 Find an orthonormal basis of the image of A.

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Q: Let [1 37 A = 2 4 Find an orthonormal basis of the image of A.

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Q: Let 1 -5 -4 A = 1 1 -1 -3 -5 Find an orthonormal basis of the column space of A. }

A: Solution:- It is given that          A=1-5-411-1-3-52

Q: It can be shown that the vectors u1 = (2,−3, 1), u2 = (1, 4,−2), u3 = (-8, 12,−4), u4 = (1, 37,−17),…

A: A basis is a subset of a vector space that spans the vector space and is linearly independent.

Q: Let S ={v1 , v2 ,...,vk } be an orthonormal basis for the Euclidean space V and {a1 ,a2 ,...,ak } be…

A: Given: S=v1,v2,,....vk is an orthogonal basis for the Euclidean space V. Also, a1,a2,...,ak is any…

Q: (c) Show that the matrices M₁ vector space M22 of 2 x 2matrices. M₂= M₁ = = 1 form a basis for the

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3 4 If a basis for R3 is B and given [*]B find i in the standard basis. =

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Q: Explain why S is not a basis for R3.S = {(0, 0, 0), (1, 0, 0), (0, 1, 0)}

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Q: 1

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Q: Let {a1,a2,...,an} be a basis of a vector space V, n 2 2. Show that {a1,¤1 +a2,...,a1 +az + · ·+ an}…

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Q: 3. Let A {v1, v2, ..., Vn} be a basis for pV and n 2 2. Is B = {v1 + v2, , v2 + V3, ..., Vn + Vı}…

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Q: Let A = {v1, v2,.., Vn} be a basis for FV and n > 2. Is B = {v1 + V2, , V2 + V3, ..., Vn + v1} also…

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Q: Let {a1, a2,..., an} be a basis of a vector space V, n > 2. Show that {a1, a1 + a2,...,ɑj + az + ·……

A: We will be using basic definition

Q: If b1, b2 form an orthonormal basis for C and x is any vector in C, then O x4- x bị x b2 0 O x+ x bị…

A: We will find out the required value.

Q: Explain why S is not a basis for R3.S = {(1, 1, 1), (0, 1, 1), (1, 0, 1), (0, 0, 0)}

A: To Determine S is not a basis for R3.S = {(1, 1, 1), (0, 1, 1), (1, 0, 1), (0, 0, 0)}

Q: 5. Consider the basis aj = (1, 2, 3), az = (2, 4, 5), and az = (3, 5, 6) for R] × 3. Consider t E…

A: Given α1 =1, 2, 3, α2 =2, 4, 5, α3 =3, 5, 6 is the basis of R1×3 So let α = α1, α2, α3 Let τ = α…

Q: Let A = {v1, vz, - also a basis for pV? How about the converse, i.e. if B is a basis for FV, is A…

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Q: (a) Let D = (2" – 1) (1, 3, 7, 15, 31,...). Note that: 1= 1, 2=-1 +3, 3 = 3, 4= -3+7, 5 =1-3+7, 6 =…

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: 3. Suppose V is a 5-dimensional complex vector space and let T € L(V). A basis for V may be chosen…

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Q: Explain why S is not a basis for R3.S = {(1, 1, 2), (0, 2, 1)}

A: To determine: The set S is not a basis of R3 S = { (1, 1, 2), (0, 2, 1) }

Q: Show that S = {(i, 0, 0), (i, i, 0), (0,0, i)} is a basis for C

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Q: The union of these two orthogonal bases (put the basis for W and W- into one set) is an orthogonal…

A: Since you have asked for part (d) and (e) , so i answered here only for part (d) and (e).

Q: Show that B = {v1=(1,0,0), v2=(3,7,-2), v3=(0,4,1)} is a basis for R3

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Q: Let A = {(0, –1,6); (–1,0,2); (2,1,0)} . Then A is a basis for

A: Introduction: A set of vectors in V is the basis of V if the set is linearly independent in V.

Q: Let 1 -6 -2 A 1 -3 1 3 -8 4 Find an orthonormal basis of the column space of A.

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Q: Determine if the set {(1,1, −1), (1, −1,1), (0,0,1)} is a basis of ℝ^3

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Q: 4 Let the basis for W is -5 -1 then the orthonormal basis for W is 1 2 3 a) 1 3/2 3/2 1 3 b) 3/2 3/2…

A: Othonarmal basis for the given basis, using Gram-schmidt Ortho normal basics form

Q: 4.13 Let {u1,u2,..., un} be any orthonormal basis of (where F R or F = C). Show that %3D Euju; = 1.…

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Q: S {1-X,1+ X,1+X2, 1}. Then S is a P1 basis for None of these P2 P4 not a basis for basis for

A: This question is related to Linear Algebra

Q: Let (₹1, ₹2, ₹3, ₹4, 25, 26} be the standard basis in Rº. Find the length of the vector x = -22₁ +…

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Q: 4 2 If a basis for R3 is B = and if a vector in the standard basis is i = |-4|, find its 5…

A: We know, The set B of vectors in a vector space V is called a basis if every element of V can be…

Q: Let -2 1 A = a- -3 4 Find an orthonormal basis of the row space of A.

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Q: -{圈[} B O B is an orthonormal basis for R?. O B is an orthogonal basis for IR?, but it is not…

A: Given B=1/21/2,1/2-1/2

Q: Find a basis for Q(3^(1/3), 3^(1/2)) over Q.

A: It is known that,

Q: Let 3 A = 1 2 -8 2 Find an orthonormal basis of the row space of A.

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Q: Lemma 2.8 B is a basis of Tiff VOETBCB: 0=U Bo

A: To show: B be a basis of τ iff for all O belongs to τ ∃ BO⊂B: O=∪BO

Q: 39. Find an orthonormal basis 1, 2, 3 of R³ such that (G) span

A: Given,                        spanu1→=span123and        spanu1→, u2→=span123, 11-1

Q: - Let 3/2 U2 = U3 a. Show that {u1, u2, u3} is an orthonormal basis for R³.

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Q: Let S = {1+4x– x², 2+5x+3x², 3x –5x², 3+15x +8x} . Does S span P,? Is S a basis for P, ? If not,…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.