Find all homogeneous polynomials of degree 3 in R² 3 p = Ax² + Bx²³y + Cxy² + Dy ³ that are harmonie.

Q: Use the inner product (p, q) = aobo + azb1 + azb2 to find (p, a), ||P||, |||, and d(p, q) for the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 3. Consider the differential equation y' +2y= 0. a) The equation above is first order linear…

A: a) write y' =dydx The equation becomes dydx+2y=0 separate the variables and write it again by…

Q: give the general formula of this amount b.) choose those polynomials that contain elements of the

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Q: Find Tay br Polynomial. for the function fox): Vx + 3. ot degree 3 centered ata=2

A: According to the problem, we have

Q: (a) Calculate the resultant of A = 3x² +3 and B = (x-2)(x+5) by hand. (b) Let A, B, C be…

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Q: Is 6 a factor of 54y + 42z? yes no

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Q: Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), ||p||, ||9||, and d(p, q) for the…

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Q: 1 2 3 3) Consider A = 0 1 2 2 31 teristic polynomial of A? a) 23 – 2:2 – 9z +3. Which one of the…

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Q: FCX)={x-3)? C12

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Q: his is some (a) Use this

A: Given  (a) y" + 3y' + 2y = f(t), y(0)=y'(O)=0. (b)f(t) = e3t and f(t) = t.

Q: Use the inner product (p, q) = abo + a,b, + a,b, to find (p, q), ||p ||, ||9||, and d(p, q) for the…

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Q: 5. if we have two polynomials pl=3x5 + 8x* – 2x2 + 4x + 1 p2= 2x6 + 3x* – x² + 4x Find:- Your answer…

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Q: (d) Z[ /2] is a field.

A: As you asked for option D.

Q: Check if f(s, t)-5s-4t s-4t is a homogeneous punction, and give its degree.

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Q: Given: [(4x + 3)²D² - 12(4x + 3)D +64]y = 16[(4x + 3)² sec² (In|4x +31)], transform it to z. A.…

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Q: Find the roots of the following equations, assigning the results to ra, rb, and rc respectively a)…

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Q: Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), ||pl|, |la||, and d(p, q) for the…

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Q: Find the integration distance (f, 9) = | f(x)g(x) dæ between the given polynomials. f(x) = 11æ – 3,…

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Q: Find the product. SHOW ALL WORK clear 10

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

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Q: Use the given LU factorization to find all solutions to Ax = b 1 0 0 0] [50 -31 1 0 0 0-8 6 9 1 0 0…

A: We have given:To find all solutions to  using the given LU factorization, we can proceed as…

Q: 4. Calculate Res z+1 z²+9 -3i

A: The answer is (1/2)+(i/6)Explanation:Step 1: Step 2: Step 3: Step 4:

Q: 10 - Which one is the highest order Lagrange polynomial of the grids below? Xị Yi -2 3 1 -1 x2—9х-8…

A: We have to solve given problem:

Q: Ifx.y,z are real numbers satisfying the equation 25(9x + y) +9:*–15(5xy + yz + 3:x)= 0 then prove…

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Q: Use the inner product (p, q) = abo + a,b, + a,b, to find (p, q), ||p ||, ||9||, and d(p, q) for the…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Use the inner product (p, q) = aobo + a¡b1 + azb2 to find (p, q), ||P||, ||g||, and d(p, q) for the…

A: Given polynomials are: p(x) = 3 - x + 2x^2 q(x) = x - x^2 We know that the inner product is given…

Q: Answers to 4.5.2 Solving Polynomials: Irational Conjugates 1) 1- V7, 2-2vi 2) -3 - Vi, 3- VE 5) flz)…

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Q: Indicate whether the polynomial is written in standard form or not. A) Standard form B) NOT standard…

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Q: a) Use Newton interpolation to find the unique cubic polynomial f that passes through the points (0,…

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Q: Exercise 8.17 1. Find the products: (a)) (x - 3)² b) d) (x-5)(x-5) e) 9) (2x-1)(3x + 1) h) k i) (5 -…

A: Let's find the products for each of the given expressions:  (a). (x−3)2(x−3)(x−3)=x2−3x−3x+9=x2−6x+9…

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Q: Q2\ Prove that Ax (B+C) = A×B + AxC When A= 2i + j-k B=i-j+ 2k Sumer C=i+2j+k

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