Consider P2 with the inner product given by evaluation at - 2, 0, and 2. Compute ||p|| and |q| for p(t) = 4t – t² and q(t) = 3 + 5t p| =(Simplify your answer.) lall =(Simplify your answer.)

Q: Exercise 2. Let f: X→Y be a map between the topological spaces X and Y. a) Let V V(x) be a…

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Q: Find the following products for p = (7,0, 2), q = (-2,2,-2), and r = (0,2,-3). a. (r p)q b. |p|l

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Q: Find the coefficients of x from the expression (x2 – ) 5 3) 10 - X.

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Q: Q1-Using the nodes (x, =2, x-=2.5 and x; =4), to find the second interpolation polynomial for flx) =

A: Given nodes are x0=2, x1=2.5, x2=4 and function is f(x)=1x Now table is x 2 2.5 4 f(x) 0.5 0.4…

Q: Evaluate as indicated. If z(t)=2x2+7t-4. find z(-6) and z(3)

A: Topic:- algebra

Q: Find k so that kt² – 5t – 12 is in span{4t² + 3, −5t² − 5t}. -

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Q: 8) a) Let A be the set of all real numbers z 0, 1, 2. Define the permutation f: A→A by the formula…

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Q: . Factor x12 -1 as a product of irreducible polynomials over Z.

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: 2. Is the following set of polynomials linearly independent in P2? Explain your work. (-1+2t + 3t?),…

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Q: (d) Compute P(x 2 2).

A: Given that  X~Poisson(μ=6) Probability mass function of X is  f(x)=μxe-μ/x!  , x=0,1,2,3,____

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

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Q: In real analysis,Prove that if A is countable, then m(A) =0.

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A: Given points are  P0=0.0, 1.0=0, 1; P1=2.0, 2.0=2, 2; P2=3.0, -1.0=3, -1 We have to find the…

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Q: > For y, polynomial x = y₁ 1 D²-2 [x²] y, = [-1-D² +...]. [2x+3]

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Q: Use Cramer's rule to find only the value of x2 , where a is a positive real number. 2x2 – x3 + x4 =…

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Q: Construct the addition table for Z5. Using this table, or otherwise, determine the following x in…

A: First we find addition table for Z5. Then find values of x.

Q: - Express P(x) = xª +.2x³ + 2x² - x - 3 in terms of Legendre's polynomials

A: In this problem, we use Rodrigue's formula to express Legendre's polynomials.

Q: Find the standard inner product on P of the given polynomials. p= -2+ 4x + a2, q = 3+ 4x 3a2. (p, q)

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Q: The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A…

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Q: Multiply (x+ 1) (x – 1) O x² - 1 O x² + 2x + 2 O x² + 1 O x2 - 2x - 1

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Q: Factor f(x) = x² - 2x³ - x² - 2x - 2 € Q[x] into two irreducible quadratic polynomials over Q. Hint:…

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Q: . Given the set of data points: X y 6 5 10 2 1 3 Set up and solve a direct interpolation polynomial…

A: Interpolation is the finding of the value between two points on a line or on a curve. For the…