1. Let S = {(1, 0, -1, -1),(1, -1, 1, 2), (5, 2, -9, -11)} CR¹. a) Show that S' is linearly dependent over R. b) Determine a basis of Span (S) and dim (Span (S)) R c) Find a basis of R4 that contained the basis of span S that you obtained in part b).

Q: Which of the following are a basis for the orthogonal complement of the span of (1,-2, -5, 1)7 and…

A: NOTE: Refresh your page if you can't see any equations. . write both vectors in the matrix

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A: Answer given below.

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Q: (- _-----«s) If {ƒ1, ..., fn} is an orthogonal basis of R¹ and U = span{f₁,..., fm}, show that U =…

A: We will be proving the statement using basic definitions of Orthogonal Basis of Rn .

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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A: A set is a BASIS if it linearly independent and spans the vector space

Q: b) Using the basis S in (a), find [T)s if ū = (2, i, 2 – i).

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Q: 2. Prove that the following vectors |v1) = (1, 1, 0) |v2) = (1, 2, 0) |v3) = (0, 1, 2) span C3. Are…

A: Given that,                    |v1&gt; = 1 , 1 , 0                    |v2&gt; = 1 , 2 , 0…

Q: 3.) Consider the following vector. O M 2 2 t 2 6 x3 = 16 -S a) Are the vectors {x₁, X₁, X3) lineonly…

A: Since you have posted multiple sub parts. according to guidelines, I solve only first three…

Q: S=CVi ,Vz, Vz, Ve) Vi=(1,2,2) V, = (3,2,1) Vz =CII,10,7) Ve = (7,6,4) find R W=span3 bosis and dim W

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Q: A) Let v1, v2, v3 be defined below. Does {v1,v2,v3} form a basis of R3?Justify your answer B)…

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Q: (11) Find the dual basis {V4.V } of the stan dard basis of IR. Let T:IR → IR defined by T(xiy, z)…

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Q: 2. The vectors v₁ = and V3 = 1 [] 2 [] 2 are a basis for the space R³. It is given that: 0 Q+A + C2…

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Q: 3. Let V be the vector space of polynomials with coefficients from R. a) Show that the following…

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Q: Consider the basis B = {{2, 1), (3, 1}} for V = R² and let {x1, x2} be the dual basis of B. Then for…

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Q: a) Give an example of subspaces U = span(f1, f2, f3) and V = span(g1,92; g3) of RaJa] such that…

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Q: Given the vectors -B-A-N U2 = = 2 1 = -plain why u₁, U2, U3 is a orthogonal basis for R³. Let L be…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: - {{:) ()(}} (3) 2 B be an ordered basis of the vector space R³. Let the vector v = Find the…

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Q: 3) li) Find the dual basis {l, l} of the standard basis of IR". (i) Fiod th

A: Since you have asked more than one question, we will solve first one for you. If you want other…

Q: 2. Let ū = (-1, 2, 1), ở = (1, – 1,–1) and w = (2, 3, 0). Find the coordinates of (2,4,4) with…

A: Using gauss Jordan elimination method to find the value.

Q: Assume that: U1= -1 -1 u2= 1 And W=span {U1, U2}. -Find a basis to W-.

A: Here   u1 , u2 are two vector. W= span {u1, u2 } So, {u1 , u2 } is a basis . Now we found a basis ,…

Q: 7.4Find a subset of the vectors v= (1, -2, 1, -1), v2= (0, 1, 2, –1), vz= (0, 1, 2, –1) and v,= (0,…

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Q: It is known that the set {a,b} is a basis in a plane. Let u = a +b and v=a-b; then (a) {u,v} is a…

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Q: Suppose that a₁,a2,..., a, form a basis of R" and y = ₁²₁ +2₂₂ + ... + n Anan with 2; = 0. Prove…

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Q: 0.1,1 ) and v (0, 0,1) is Basis of R3 Not spannig Linear dependent

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Q: 5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1,0,0)T., (2,0, 1,0), and (0, 0, 0, 1) form a…

A: The given set is .Now

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

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Q: 3) Let (v,, vy, v) be a set of vectors from a vector space R', then: a) The vectors are linearly…

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Q: Show that the vector space P, has the basis S = {1, x, x², x³}. %D

A: We have to solve given problem:

Q: Let {u1, ·.., Un} be a list of vectors in an n-dimensional vector space V and let B be a basis for…

A: Given V is a n- dimensional vector space. Let B be a basis for V. Let B=v1, v2, …, vn. Let u1, u2,…

Q: Which of the following subsets of R* is basis of R*. B1 = {(1, 0, 0, 0), (1, 1, 0, 0), (1, 1, 1, 0),…

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Q: 1) We write vectors horizontally for this problem. Let U be the subspace of IRS defined by U =…

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Q: Let M be a subset of R2 and M = { (1,2), (1,1) } Find Span (M) (1) Show that if Mis linearly (2)…

A: Given M is a subset of R2 and  M = {(1,2),(1,1)}

Q: Suppose {v1, v2, V3} is a basis for R³. Span {v2 – V1, V3 – V1} is a plane in R³. [Hint: What can…

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