The set B = {322 – 4, 15x² – (20 + 2x), 38 + 4x – 27x²} is a basis for P3. Find the coordinates of p(x) = 144 + 16x – 102z2 relative to this %3D basis: [p(x)]B=

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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…

A: Solution :-

Q: 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x²,1 + x + 4x²,1 – 7x

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

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Q: Find the coordinate vector of x2 + x - 17 relative to the basis {x² + 1, x + 2, x - 3}.

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Q: (a) Find the basis for the solution space of I1 +a2 - a3 = 0, -2.r1 - 12 + 5rz = 0, -21 + 4r3 = 0…

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Q: Do the polynomials x2 + 1, x? – 1, 2x – 1 form a basis in P2

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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: In P,, find the change-of-coordinates matrix from the basis B= {1-2t+t?,3- 5t + 4r,2 - 2t + 5t?} to…

A: Given basis's of P2 are B=1-2t+t2,3-5t+4t2,2-2t+5t2 & C=1,t.t2.

Q: The set B = {2 – 4x?, 8+ 3x – 16x2, 21 + 9x – 40x²} is a basis for P2. Find the coordinates of p(x)…

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Q: Consider the real quadratic form q : R’ → R, defined via: q(x1, x2, X3) = x + 25x; + 125x + 10x1x2 +…

A: Solution

Q: Question 2. Are the polynomials x2 – 2x + 1, 2x2 – 3x – 6, -x² + 5x – 3, Зд2 + 8х — 6Е P2: b) a…

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Q: Q1. Show that the first four Laguerre polynomials [named for the French mathematician Edmond…

A: The first four Laguerre polynomials are 1, 1 - x, 2 - 4x + x², 6 - 18x + 9x² - x³.

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Q: The vectors 11 v1 = -4 V3 4 -5 form a basis for R° if and only if k +

A: The vectors are basis of R3 if they are not linearly dependent.

Q: In P, find the change-of-coordinates matrix from the basis B= {1-2t +12,3 - 5t + 412,2 - 2t + 5t?}…

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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: Consider P2(R) with its basis B = (x, x + 1, x² –- 1). Find [x2 + 3x + 5]B.

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Q: Find a basis for the subspace 96 4a + 6b W = E R2x2 a, b eR} of R2x2- 86 5a Ex: 1 4 6. A basis for W…

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Q: a) Find the basis for the solution space of I1 +a2 - r3 = 0, -2r1 - 12 + 5r3 = 0, -11 + 4r3 = 0 %3D…

A: (a) given system of linear equation x1+x2-x3=0-2x1-x2+5x3=0-x1+4x3=0 to find - basis for solution…

Q: b) Find the value of k such that (-1,1,1), (1,1,1), (1, -1, k) form a basis of R²

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Q: Find the basis for the solution space of I1 + x2 – 13 = (0, -2r1 – 12 + 5r3 = 0, -*1 + 4r3 = 0 and…

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Q: The set B = {3x² – 4, 152² – (20 + 2x), 38 + 4x – 27x²} is a basis for P. Find the coordinates of…

A: Given, the set B=3x2-4,15x2-20+2x,38+4x-27x2 is a basis for P2. We have to find the coordinates…

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: (c) Find a basis for the row space of A.

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Q: In P2, find the change-of-coordinates matrix from the basis B= {1-2t + ?,4 - 7t + 52,5- 8t + 81?} to…

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Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

A: Consider the coordinate matrices of “x” relative to a non standard basis B=4,-1, 0,1 for ℝn  and…

Q: Let B = {x²+x,-2x² + 3x + 3, 2x² – x – 2} be a basis of P2(R)

A: Given,            B=x2+x,  -2x2+3x+3,  2x2-x-2

Q: . ) The set B = {4x² – 4, 4x – 20 + 20z², 37 – 8z - 36x²} is a basis for P. Find the coordinates of…

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Q: The set 1 [O 01 B : is a basis of the space of upper-triangular 2 x 2 matrices. -3 -27 Find the…

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Q: If {x, a} is a basis of solutions of a?y" + axy' + by = 0, then a = (A) -2 (в) 2 (C) -3 (D) 3 (E)…

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Q: y" + ay' + by = 0 for the given basis. -4.3x 16. e2.6x

A: We have to find the ODE for the given basis.   According to our guidelines we can solve only one…

Q: Let V = P4(R). Find a basis of V containing the polynomials p1(x) = 1 + 2x-x 2+3x 3+2x 4 , p2(x) =…

A: The detailed solution of the problem is given in the next steps.

Q: - 3x3 + 7x4 = 0 X1 -7x2 - 4x4 = 0

A: The solution are next step is..

Q: 6. Find a polynomial p(x) for which {r² – 1, x² +x +2, p(x)} is a basis of P2(R).

A:

Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

A: Given B=3,-1, 0,1 xB=23

Q: Suppose that A = [c, c2 C3] is a 3 × 3 matrix with columns c;, and suppose that a basis for the…

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Q: Find a basis for R³ including as many columns of A as possible.

A: First we will find the column space of A and then we will extend the column space of A into the…

Q: Q1. Show that the first four Laguerre polynomials (named for the French mathematician Edmond Laguere…

A: We know that the set of all polynomials with real coefficients and degree atmost 3 is a vector space…

Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for Rn, find the coordinate…

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Q: In P2, find the change-of-coordinates matrix from the basis B=(1-3t+12,2-5t+31²,3t+41²) to the…

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Q: In P2, find the change-of-coordinates matrix from the basis B= {1– 2t + t?,4 - 7t + 5,2 - 2t + 5t?}…

A: See the detailed solution below.

Q: Q1. Show that the first four Laguerre polynomials [named for the French mathematician Edmond…

A: Result: If dimension of a vector space V is n then any linearly independent set containing exactly n…

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: Find the matrix of T(ax + bx + c) = (a - b)x² + 2cx with respect to the basis {x, x, 1} of P2. Use…

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