You are given that B = {1 – x², 1+ x, 2x + 3x²} is a basis for P2 and - 2 [p(x)]B= |3. If p(x) = a + Bx + 8x?, what is the value of 8? 8 O 5 07 O 13 O 12

Q: Using the first four Hermite polynomials as a basis for P3, find the linear combination for the…

A: In this problem ,we use the concepts of linear combination.

Q: 6. Find all the roots of the following polynomials: a) p(r) = * - 3.r" +?+ 7x – 30 and b) p (r) = r*…

A: Note: Since we are allowed to solve one question at a time, we have solved the first one. Kindly…

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Q: Which of the following is equal to (2° – 7æ)*dx = (x6 -

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Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

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Q: (b) Let L: M2x2 → M2x2 such that L(A) = At. Find the matrix repre- sentation of L from [L]s,s=

A: Given Given  such that .Find the matrix representation of L from S.

Q: Is the following statement correct or incorrect: The matrix notation of the quadratic form Q (xı,…

A: Solution : Given 2 variable quadratic form is                     Q(x1,x2)=5x12-10x1x2+x22 We have,…

Q: . Let 21 2i and z2 = 1+v3i. (a) Express zi and z2 in mod-arg form. (b) Plot in the complex plane the…

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Q: [1 2 [1 0 3 andC = 2 1 1 1 1 2 31 1 1 a) LetA =|-1 2, B = 2 2 1 . If possible, -2 1l |1 3 -1 -1…

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Q: Determine which of the polynomials below is (are) irreducibleover Q.

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Find the coefficient of x3y2z3w in the expansion of(2x + 3y − 4z + w)9.

A: The given expansion is 2x+3y-4z+w9. We have to find the coefficient of x3y2z3w.

Q: Find bases for the null space and row space of A. 5. 8. -7 -4 -1 -8 1 3. 3 A = -1 0. -1 1 -2 4 7. 10…

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Q: Does the following set of polynomials {t? + 1, t2 + t,t + 1} span P2?

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Q: Use nested multiplication algorithm to convert the polynomial 1+2x+3x² into its equivale Newton form…

A: In this question, the nested algorithm to convert the polynomial 1+2x+3x2 into its equivalent Newton…

Q: If x, y, z are the three factors of a³ – 7a – 6, then value of (x + y + z) will be

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Q: Let a=⟨−3,−2,2⟩ and b=⟨−4,−2,0⟩ Compute:

A: Given that          a = <-3, -2, 2 >    and    b = <-4, -2, 0> Here we have to compute…

Q: Find the QR factorization of A = R = Ex: 1.23 0 -1 -4 -2 0 0 3 1 0 given Q 0 -0.24 -0.97 -0.99 -0.12…

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Q: Determine the product of the following: (x - 3) (x + 7) O x2 – 4x + 21 |- O x? + 4x – 21 O x - 10x +…

A: The given equation is:    (x-3)(x+7)

Q: If the sum of the coefficients of all even powers of x in the product (1 + x + x² + ... + x2n) (1 –…

A: Introduction :

Q: Consider the matrices: 7 A = B = С — -6 6. D = [6 8 3], E = | 5 3 6. -6 3 F =| 3 9 G = 3 -3 5 3 7 5

A: In this question given that any type of metrix and help of these metrix we find the value of any…

Q: Consider the polynomial p(z) = z + 4z + 8. Evaluate it at the following values: (a) z = (b) z 2i 3 –…

A: We need to put the given values at the place of z

Q: Expand the f(x) = 10 + 8x +9x² in a seried of Legendre polynomials. O a 13P,x)– 8P,(x) – 6 P, (x) O…

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Q: Find, if possible, A + B, A- B, 2A, 2A- B, and B + A = 5-6 2 3 -4 1 (a) A + B 183 11 (b) A - B 188…

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Q: 2х1 + 3x2 — хҙ — 2 Зx1 — 2х2 + Xз — —1 -1 %3D -5x1 4x2 + 2x3 = 3

A: Consider the provided equations, 2x1+3x2-x3=23x1-2x2+x3=-1-5x1-4x2+2x3=3 Solve the above equation by…

Q: Consider the homogenous polynomial ai + 10r1r2 + x². Find a suitable substitution s = Question 3 azi…

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Q: 3. Find bases for the nullspace and row space of A. 6 4 -1 -2 5 7 A = 1 3 -1 2 4 5 1 -2 0 3 9 -1 -1…

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Q: If then A-¹- = A = [1 0 0 07 3 1 0 0 24 1 0 8 55 1

A: The given matrix, A=1000310024108551 We have to find an inverse matrix of A.

Q: 1 2 and B ol: Compute the following: 2A, A – B, AB, and BA. Let A -3 1

A: Given problem:-

Q: 4. Find z, and z, such that, 2iz, +iz, 2+5i and = 9-11i 3i z,-2i 2, 4 =i+1, z, = 3+4i (b) z, = 3-4i,…

A: Solution:- let z1 and z2 be the different ccmplex number i2= -1 i3=-i

Q: .

A: Given

Q: Let à = (0, 3, 2), b = (3, 1, 1), and c = (2, 6, 3). a Compute the following: = (a - b) (à · c) :…

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Q: 31 Let A =-1 4 and B = 3] 2 [3 -1 . Compute the (3, 1) entry of AB.

A: Given: A=23−1403  and  B=3−13124[AB](3,2)=?[AB](2,3)=?

Q: Which of the following sets of polynomials span R2 O A and C O A, B and C A and B B and C O A =…

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Q: 1 a) Let A =-1 [1 0 3 and C =2 1 l1 31 [1 2 1 1 B = 2 2 1 If possible, -2 1] li 3 -1] 1 compute (A"…

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Q: Given (xi , xi2022 i ) ∀i = 0, ..., n, where x0 = −1, x1 = 0, x2 = 1, x3 = 2, ..., xn = n − 1. Write…

A: Given xi,xi2022∀i=0,1,2,...,n  Where x0=-1, x1=0, x2=1, x3=2,..., xn=n-1