transformation from R³ to R² such that [7] = (5 3), where B = {(1,0,0), (0,1,1), 5 1 5 4 Let T be a linear (0,2,3)} is a base of R³ and C is the canonical base of R² respectively. c) Calculate a basis for the image of T

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

Q: isider the complex number 3 a = 4+i√2, where i² = -1. (a) Find the minimal polynomial of a over Q.…

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Q: Show that ?? = {(1,2,3), (−1, −1,1), (5, −4,1)} is an orthogonal basis of ℝ3, and use the Fourier…

A: Definition: A subset of a vector space V is linearly independent, if  Theorem: If is a orthogonal…

Q: Q8) Explain why S is not a basis a) S = {(2,1,–2), (–2, –1,2), (4,2, –4)} for R³ b) S = {2,2,x +…

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Q: 5) B = [(1, 2, 0)T, (1, 1, 1)T, (1, 0, 0T)] is an ordered basis for 3. a) Find [v]B, the coordinates…

A: A change of basis consists of converting every assertion expressed in terms of coordinates relative…

Q: Let W = } t s,t e R -S - 31 5) Show that -6 is in W+. 3 6) Find a basis for W+.

A: given W=s+3tt-s-t  , s t ∈R

Q: 5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R³,…

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

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Q: (a) determine whether the set of vectors in Rn is orthogonal, (b) if the set is orthogonal, then…

A: The given vectors are 35, 45, -45, 35. We have to determine whether the vectors are orthogonal,…

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Q: Let V=R? and let (R?)* be the dual space for R². Subtask (a). Find the basis {d1, þ2} that is dual…

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Q: {B].[B]} Vector w expressed in ß is w = Vector v expressed in basis a = = {[]·[3]} Answer: 133 Wa is…

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Q: bị and B := E R³, consider the inner product on R³ defined For a := a2 b2 b3 a3 by (a, B) := (2a1 +…

A: We find the matrix of inner product by finding each possible innner products. The orthonormal basis…

Q: (0+0i) 0+0i 1+0i 0+ 0i 0+0i (1+0i is the standard basis for Cn as a vector space over C and again…

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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 Determine whether the vectors form a basis for R*. (You may use any relevant theorem that we have…

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Q: B = [(1, 2, 0)T, (1, 1, 1)T, (1, 0, 0T)] is an ordered basis for 3. a) Find [v]B, the coordinates of…

A: Given that B = 1 , 2 , 0T , 1 , 1 , 1T , 1 , 0, 0T is an ordered basis for ℝ3 .  We have to solve…

Q: A basis of {(a, b, c, d) : b = 6c + d, a = 0} (A) {(0,0, 1, 0), (0, 6, 0, 0), (0, 0, 0, 1), (0, 1,…

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Q: 1) A) Let T: 1R²_) 1R²³ be defined by T (ar, az) = (90-92, 90, 200+92). Let B be the standard…

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Q: A basis of {(a, b, c, d) : b = 6c+ d, a = 0} (A) {(0,0,1,0), (0, 6, 0, 0), (0, 0, 0, 1), (0, 1, 0,…

A: We have to check

Q: 7) The vectors. A) True 13 False 17 -19 + -34 38 17 2 form a basis for n

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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: Recall that IR2 is equipped with the dot product. = {01,02} - {[2³] · [ 3 ]} ₁ be an orthogonal…

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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: Find an orthogonal and an orthonormal basis for 5 1 2 W = Span Spa { ·} 0 2 -2 -4 0

A: GRAM-SCHMIDT METHOD The Gram-Schmidt process (or procedure) is a sequence of operations that allow…

Q: Be S = {v1 = (1, 2, 1), v2 = (2,9, 0), v3 = (3, 3,4)} a subset of R and T: R → R? T(v1) = (1,0),…

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

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