Following question is from a linear algebra course, We consider a second basis of V, C = {1 + X, X + X2, X2 + X3, X3}. (You don't have to prove that C is indeed a basis of V). Show what the image under fC is of: • the four basic elements: Q1(X) = 1 + X, Q2(X) = X + X2, Q3(X) = X2 +X3 and Q4(X) = X3 • P(X) = 2 + 6X + 3X2 + 4X3

Q: The set B = {3+4x², 12 − 3x + 16x², 9x - 25 - 36x²} is a basis for P₂. Find the coordinates of p(x)…

A: Here we have to find the coordinates of p(x) relative to the basis B.

Q: where B A = = H (a) Find At -6 rref (A). -1 -2 TATT -1 7 -4 -18 10 9 NAAN -1 1 -3 2 17 (e) Find a…

A: (.) Note: '' As per guidelines we will solve first three subparts. If you want any specific subpart…

Q: What is the basis and dimension of M3(R)?

A: Basis: For a vector space V, the set of linearly independent vectors that generate the whole vector…

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: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

A: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

Q: The set B = {4+x², 20 - 3x+5x2, 45-6x + 11x2} is a basis for P2. Find the coordinates of p(x) = 6x -…

A: 30-1Explanation:

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

A: Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

Q: {(:}) (::). (; })· (; )} 1 1 1 2 2 3 3 4 2 2 3 4 5 1 7 3

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Q: Consider the bases for M2x2(R) given by a' : and a the stan- dard basis. For the transformation T :…

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Q: } 4. You are given that B = {1– 2x + x?, x+ x?, 2 +x – a?} is a basis for P2. (i) Find the…

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Q: a) Let q(t) = 4t2 + 2t + 9 be an element of P2. Write the coorfinate vector of q(t) relative to…

A: We have to find the followings ; (a) We have to find the coordinate vector of  q(t) = 4t2+2t+9 with…

Q: The set B = {4x? - 1, z -3+ 12z2, 12 – 3x 40x} is a basis for P2. Find the coordinates of p(x) = 52…

A: write each polynomial as a vector  4x2-1=x2x140-1 12x2+x-3=x2x1121-3 -40x2-3x+12=x2x1-40-312 write…

Q: Computations: [7x -3y 9. Compute a basis of x, y E R x + y

A: We will find out the required basis.

Q: The set B = {3 + 2x², 6 − 2x + 4x², 4x − 13 – 10x²} is a basis for P₂. Find the coordinates of p(x)…

A: The objective of the question is to find the coordinates of the polynomial p(x) = 18x - 54 - 40x^2…

Q: Consider the following ordered basis for P₂ (R): B = {x² + 2x + 1, x + 1, 1} (a) The quadratic…

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Q: please explain part d because i am confused by the second and third part of part d.

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Q: Following question is from a linear algebra course, We consider a second basis of V, C = {1 + X, X +…

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Q: Extend {l + x, 1 + x + x2} to a basis for P 2.

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Q: now that B = {x, r³ + 2x² + 4, x² + 2, 1} is a basis for P3.

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Q: The set B = {− (1+3x²), − (2+2x+6x²), − (6+4x+21x²)} is a basis for P2. Find the coordinates of p(x)…

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Q: 3. For each of the following pairs of ordered bases ẞ and ẞ' for P2(R), find the change of…

A: To find the change of coordinates matrix from a basis β′ to β for the vector space VThe identity…

Q: etermine whether the set S = {1-3xr?, 2x+5x²,1-x+3x²} is basis for P,(R).

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Q: ow that B = {5+i, 2+i} is a basis for Q(i) whose elements are algebraic tegers. Why is ß not an…

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Q: The set B = {4- 2x², 12 + 3x − 6x², 18x² - (35 + 6x)} is a basis for P₂. Find the coordinates of…

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