2. Let ū = (-1, 2, 1), ở = (1, – 1,–1) and w = (2, 3, 0). Find the coordinates of (2,4,4) with respect to the basis ū, i and w.

Q: Find the coordinates of the vector v = (7,4) with respect to the basis U₁ = (2, 1) and u₂ = (3,1).

A: The answer is given below:

Q: Find the matrix A′ for T relative to the basis B′.T: R3→R3, T(x, y, z) = (x + 3y, 3x + y, −2z), B′ =…

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Q: Prove that the vectors (1. 1. 0) (1 2 3) and (2. –1 5) form a basis for R3

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Q: Consider the following two ordered bases of R³: B C = a. Find the change of basis matrix from the…

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Q: Let B = (1, x + 8, (x – 1)², 5x³) be an ordered basis for P3. Find the coordinate vector of %3D f(x)…

A: We have used the standard basis C {1,x,x^2,x^3} to write the coordinate vectors for f and each…

Q: Given the vectors X1 2 X2 = 3 X3 = X4 = 2 5 3 (a) Are x1, X2, X3, and x4 linearly independent in R'?…

A: Basis : A collection of vectors of R³ is said to be basis of a R³ if  They are linearly…

Q: Find the coordinate vector of p (x) = 1 + 2x + 3x2   with respect to the basis ẞ = {l + x, 1 -x, x2}…

A: Here given

Q: 3 Find the coordinate vector of a with respect to the basis B for R3. 2 1.

A: We find the coordinate vector.

Q: Find a basis for null(T), where T : R^3 → R^2 is defined by T (x, y, z) = (−7x + 2y − 5z, 4x + 9y +…

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Q: Let, T : R' → R';T(x, y,z) = (x + y + z,2y+ z,2y+ 3z) 5. Determine the matrix representation of T…

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Q: Explain why S i not a basis for P2. S = {1, 4x, -5 + x?, 3x} O sis linearly dependent. O s does not…

A: We have to find out

Q: Prove that the components of a vector x in a given basis {ê¿} are unique. That is, show that if you…

A: We will prove the given statement.

Q: Find the coordinate vector of p relative to the basis S = {p1, P2, P3 } for P2. p = 2 – 3x + 2x² ;…

A: Question from linear algebra.

Q: Let (vi..... vn) be an orthogonal basis of R". For any vectors x, y in R" show that (x- vi) (y vi)…

A: Given v1,v2,…,vn be an orthogonal basis of ℝn. Let x,y∈ℝn. Since v1,v2,…,vn is basis, therefore:…

Q: Let S = y1 be a basis of R and x = E R4. What are the coordinates of x with %3D >Y2 = respect to the…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 > R2, T(x, у) 3 (x — у, 2у - х), в' %3D…

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Q: Determine whether the vectors u = (i, 2, 3i), v = (0, i, 2), w = (1, i, 1) span C3 over C. Are these…

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Q: Let S = {u1, u2, U3, U4} C Rª, where (1,1, 1, 1), и2 %3 (1,1, —1, —1), из —D = (1,–1,1, –1), (1, –1,…

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Q: 1. Let {V1,... , Vn} be an orthogonal basis of R". For any vectors x, y in R" show that (x . V;) (y…

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Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (5x + 4y, 4x + 5y), B′ = {(12,…

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Q: 5/ Find the coordinates of x = with respect to the basis consisting of uj = (1, 3, 2), u2 = (2,…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the matrix A' for T relative to the basis B'. T: R2 → R, T(x, y) = (4x – 3y, 5x), B' = {(-2,…

A: We have to find the matrix A' for T relative to the basis B'.

Q: Find the coordinate vector of p(x) = 3 - x + 4x2 with respect to the basis B = {1, 1 + x, -1 + x2}…

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Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (-8x + y, 8x – y), B' =…

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Q: Let U = {{x, y, z) E R3|x - 3y + 2z= 0} Find a basis for U. You must explain your method, then…

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Q: Determine whether the set S {1 – t, t, 1 + t²} a. Spans P2 b. Is linearly independent c. Is a basis…

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: The following vectors u,, u,, and u, form an orthonormal basis for R³. (금이) u, = (0, –1, 0), u2 = 0,…

A: We find the required linear combination

Q: Let W = {ax? + (b-a)x + (a+b)| a, b e R}. Find a basis for V and find the coordinate vector for v =…

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Q: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

Q: 4. Let {V1, ... , Vn} be an orthogonal basis of R". For any vectors x, y in R" show that Σ (х - V,)…

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Q: Find x with respect to the standard basis corresponding to the coordinate vector [x] and basis B. B…

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Q: Find the coordinate vector of = -1 with respect to the basis B = for IR3. 2 B

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Q: Let B = {1+t,1 – t} and C = {4, 1 + 5t, t²}. Does B form a basis for P2?

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Q: Find x with respect to the standard basis corresponding to the coordinate vector [x]g and basis B. 2…

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Q: 17. Let u= (1,-1,0) and v= (1,2,1). (i) Verify that u and v are linearly independent. (ii) Extend…

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Q: Let s = {(r² –3r+4, 2r-5, x²+1} be a basis for P2, let q E P2. If (q). = [2,-3, 1], then q = %3D %3D…

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Q: Find the coordinate vector of Prelative to the basis S = {P,P2P3} P1 = 1+ x + x, P2 = x + x²,P3 =…

A: Vector

Q: Find the coordinate vector of p(x) = 5 - 2x + 4x² with respect to the basis B = (1 + x, 1 – X, x?}…

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Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x2} || O sis linearly dependent.…

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Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x²} O sis linearly dependent. O…

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Q: Q: Find a representation of Jp(t)> at a time t +0 using the ordered basis {|e1>, ]e2>, ]e3> }.

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Q: Explain why S is not a basis for P. S = {1, 2x, =7 + x², 9x} O S is linearly dependent.

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Q: 3 Find the coordinate vector of x = -2 with respect to the basis B for R3. -2 6 ||

A: Given that the vector x→=3-2-2 and the basis is 166,01-5,001. It is required to find the coordinate…

Q: Let {f1, f2, f3} be the dual basis of {e1, €2, €3} for R³, where e₁ = (1, 1, 1), €₂=(1,1,−1), Find…

A: Given basis are e1,e2,e3 of R3 where e1=1,1,1e2=1,1,-1e3=1,-1,-1 Its dual basis are f1,f2,f3 We have…

Q: Find the standard matrix A and A' for T = T2 • T1 and T' = T, ° T2, where T1:R2 → R³,…

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Q: Let B = (1, x + 2, (* – 1)", 9x) be an ordered basis for Pg. Find the coordinate vector of f(æ) = 8a…

A: Answer

Q: a) Find , \pl, d (p, q), and then find the angle between them for the polynomials in P2 if p(x)…

A: a) given polynomials belong to P2 , so their basis set will be {1,x,x2}  p(x)=-3x2+2x-5 =(-5,2,-3)…

Q: a) Find the coordinate vector of x = of R³. To with respect to the ordered basis *- {0-1-8} E [x] E…

A: as per the guidelines I am answering only first question (a) Let the coordinate vector of x=2-40…