Let B be the basis of P, consisting of the Hermite polynomials 1, 2t, - 2+ 4t, and - 12t + 8t°; and let p(t) = - 3+41 - 8t°. Find the coordinate vector of p relative to B.

Q: The set B=(3+2x², 12+2x+8x²,- (29+6x+20x2)) is a basis for P2. Find the coordinates of p(x) = 8 + 4x…

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Q: Let B be the standard basis of P₁, and consider the basis B' [T]B¹,B. = {(1)· (9)}< of V. Find

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Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2- 4t +t, and let…

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Q: B = {1+t²,t +t?, 1+2t +t²} is a basis for P2. Find the coordinate vector of p(t) = 1 + 4t +7t²…

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Q: Which of the following vectors form an orthogonal basis? BBE • BBA 2 3 [0 a) 1 b) 2 3 2 c) 12 d)…

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Q: Let B be the basis of P2 consisting of the first three Laguerre polynomials listed in Exercise 22,…

A: Given pt=7−8t+3t2. We have to find the coordinate vector of p relative to B. Let the first three…

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: Consider the basis D = {(1, 1, -1), (2, 1, 3), (-1, 2, 1)} of R3 and the vector v = (1, 1, 1) in R3.…

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Q: Find the coordinate vector [p(x)]B of p(x) = x² + 4x + 4 with respect to the basis B = {x³ + x – 2,…

A: According to the given information, it is required to find the coordinate vector.

Q: Suppose p= 5x?+2x +3o figure out the coor olicuate relative to the follewing basis for 29 pi =i, Pz…

A: Given p=5x2+2x+3 and basis  p1=1p2=1+xp3=1+x+x2

Q: Given the ordered basis B = {p1 = 9 + 2æ, p2 = -4 – x}, find [p]B, the coordinates of p = -39 – 9x…

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Q: For each of the B bases below, represent the vectors in the coordinate system of the C basis. 3= а.

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A: To find the coordinate vector

Q: Consider the basis B of R consisting of vectors and Find x in R whose coordinate vector relative to…

A: Basis is defined as the linearly independent set that span a vector space V. Any vector of V can be…

Q: Let B be the basis of P3 consisting of the Hermite polynomials 1, 2t, - 2 + 4t“, and - 12t + 8t°;…

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Q: {( a + b+c+d b – c+ 2d а + 2с — d H = : a, b, c, d e R } C R³, and consider --(}) u = 1 (а) Is u E…

A: Given, H=a+b+c+db-c+2da+2c-d: a,b,c,d∈ℝ⊆ℝ3      ⋯⋯(1) a) Given, u=111 Consider the system,…

Q: Let B be the basis of P2 consisting of the Laguerre polynomials 1, 1 -t, 2 – 4t + t2, and let p(t) =…

A: Let β=1,1-t,2-4t+t2 be the basis for P2R For Pt∈P2R , can be written as linear combination of…

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 vector x determined by the given coordinate vector [x]R and the given basis B. - 1 1 3 - 2…

A: To find  The vector X determined by the given coordinate vector [X]_B and the given basis B.

Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector of f(x) = - 823 6x? –…

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Q: The set B = {1 – t2, t – t², 2 – t + t²} is a basis for P2. Find the coordinate vector of p(t) = 1+…

A: The coordinate vector of p(t) relative to B will be [p(t)]B

Q: 1. Find [p]a, relative to the basis 3 = {P1. P2: Ps} for P, where p = 4- 3x +x², P1 = 1, P2 = X, P3…

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Q: Consider the polynomials p₁ (t)=3-t³, p₂ (t)=2-t², p₂ (t)=t-5t², and p₁ (t)=7-t+3t² −1³. 3 Is {P₁,…

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Q: The set B = {4 – 2x2, 20 + x – 10x2, 28x2 – (55 + 3x)} is a basis for P2. Find the coordinates of…

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Q: The set C = {1+ t²,t +t², 1+ 2t + t²} is a basis of P2. Find a vector q e P2 such that [q]c

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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: Given the basis B = the basisi B | {Q.B]} Find the change of coordinates matrix from the standard…

A: We find required matrix.

Q: Given the ordered basis B = {p1 =1– 1, P2 = 4 – 7x find [p]B, the coordinates of p = -7+ 10x with…

A: Follow next step

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

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Q: The set B = {1+t²,t +t²,1+ 2t + t?} is a basis for P2. Find the coordinate vector of p(t) = 1+ 4t +…

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Q: Let B be the basis of P, consisting of the Hermite polynomials 1, 2t, -2+ 4t2, and - 12t + 81°, and…

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Q: Q2) Find the coordinate vector [x]B of x relative to the basis B={b1, b2} bị -31 X =

A: We are give: B = {b1,b2} where b1 =(-1, 2)T and  b2 =(-3, 5)T Also,  x1 =(-1, 3)T  We need to find x…

Q: Given the vectors V1 = (x, 1,1), V2 = (1, x, 1) and V3 = (1,1, x). S = { V1, V2, V3} of the set Find…

A: 3 vectors form a basis of R3, if they are linearly Independent. Vectors are linearly Independent if…

Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2-4t+t, and let…

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Q: - - The set B = {x² - 2, 4x² − (8 + 3x), 15x² − (28 + 9x)} is a basis for P₂. Find the coordinates…

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Q: .2 The set B= {1 +t,-t-t,1+2t+t} is a basis for P,. Find the coordinate vector of p(t)= -3-5t-6t…

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Q: B = {3 – 3x, 9 – 2x – 9x², 13 – 4x – 12x?} is a basis for P2. The coordinate vector of p(x) = 4 + 2x…

A: We have to find the coordinate vector of P(x)=4+2x-6x2. w.r.t the basis…

Q: Given basis B = {(1, -1), (2, 3)} and basis C = {(1, 0), (0, 1)}, and linear map T = (x + 2y ; 2x -…

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Q: Prove that B is a basis of V.

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Q: Which of the following vectors form an orthogonal basis? a) b) 12 d) None of these 6. 6. 6.

A: We have to find which of the following vectors forms an orthogonal basis.

Q: Find [ℚ(sqrt2, i ) : ℚ] and a basis for ℚ(sqrt2, i ) over ℚ.   [Hints: Use the degree and a basis…

A: Find ℚ2,  i: ℚ and a basis for ℚ2,  i: ℚ over ℚ.

Q: Given vectors v1 = (3,0,0), v2 = (1,2,0), and v3 = a) Are the vectors linearly independent or…

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Q: Find the coordinates of x in the ordered basis B = (a, b). %3D [2]B =

A: Consider the vectors: a=-7-2, b=7-2 and x=-2-5. As the ordered basis is B=a, b=-7-2,7-2, we have…

Q: 1. Find [p]8, relative to the basis B = {p1, P2, P3} for P2 where p = 4 – 3x + x², p1 = 1, p2 = X,…

A: Q1. p = 4 - 3x + x² = (4)p1 + (-3)p2 + (1)p3  So, [p]β = [4   -3   1]

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…

Q: The set B = {x² – 2, 4x² − (8+3x), 15x² − (28 + 9x)} is a basis for P₂. Find the coordinates of p(x)…

A: Result: Let B be the basis of P2 and let p(x)∈P2. Then the coordinates of p(x) relative to the basis…

Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2- 4t + t, and let…

A: Find your answer below

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.