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: 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 a x b, and c* (a x b) a = 2i + 3j - k, b= -1 + 4j + 5k, c = 2i + 3j + 4k Show all steps

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Q: Let z = x +3xy+ 2y . Find and

A: Given function is z= x^2 +3xy +2y^2

Q: Find the product D (xD – 3) A) xD²– 2D B xD²+4D (c) xD² – 3D D xD²+3D

A: .

Q: 2. Given the points (1,0.7),(2,0.73),(3,0.8),(4,0.75),(5,0.6). Use Lagrange polynomials to find the…

A: Given points are xi 1 2 3 4 5 yi 0.7 0.73 0.8 0.75 0.6 Here, i=0, 1, 2, 3, 4.

Q: da Use a trig substitution to evaluate x2 V9- x

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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: Let p, = 2t – 1 and p2 = t3 +2. Write three polynomials that are in span{p1, P2}-

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Q: Evaluate SA=_dx where A = x ² + 8x-3 and B=x²+3x²

A: To evaluate the following integral.

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

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Q: The characteristic of Z6 x Z, is 18.

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Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

Q: Verify the factorization using the FOIL method. (x + 3y)(x – 7y) = x? – 7xy + 3xy – 21y² = x² – 4xy…

A: The given expression is: x+3yx-7y=x2-7xy+3xy-21y2⇒x+3yx-7y=x2-4xy-21y2    -1 Thus, we have:…

Q: The polynomial z + pr + qr + ra + 6 is exactly divisible by each of (z 1). (z - 2) and (z-3). Find…

A: Given,

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: Find the QR factorization of A = R = Ex: 1.23 0 4 -2 0 1 given Q = 0 -0.99 -0.12 -0.24 -0.12 0.96…

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Q: Factor completely. qs - 8s + qf - 8f qs - 8s + qf - 8f =

A: We have to complete factor

Q: If x? – 2x – 3 = (x+ A)² – B² , then the value of Bis %3|

A: Given that   x2-2x-3=(x+A)2-B2,  we have to find the value of B. To solve the problem we first…

Q: Determine Q(x) when P(x)=x³-5x2-3x+2 is divided by x-1 and then expressed in the form Select one: O…

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Q: Find m so that x– 5 is a factor of f (x)= 4x² – 21x² +mx–15.

A: Consider the given polynomial fx=4x3-21x2+mx-15

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

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Q: [7 0] Consider A = 5 7 and find AA" and ATA and AA"A or explain why these products do not exist.

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Q: а. (4D + 1)(D — : с. (D — х)(D + х)

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: L{t(u0 – u1) + t²u1}.

A:

Q: Let ā = (−4, −5, −3) and 6 = (-5, −4, 4) Find a × 6. V >

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Q: Evaluate dxdy √√3x + 4y over the rectangle [0,3] × [0,4].

A: We find required integral by using Fubinis method.

Q: find the missing P and Q (x+P)(x+7)=x2+15x+Q

A: Given

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: - 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: Q3- If A = 4i + 2j – 3k , B = 5i + 2j – k Find |A X B|

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Q: 8. Find the polynomial equation for: -3 (-2,0) (-1,0) 0 N (0, 1.6) (0.333,0)

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

A: Solution:

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

A: