Let Po, P1, and p2 be the orthogonal polynomials described below, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, and 2. Find the orthogonal projection of t³ onto Span{p.P₁.P₂}- Po(t) = 2 P₁(t) = 4t P₂ (t) = 1²-2 The orthogonal projection of t³ onto Span{P.P₁ P₂} is | (Simplify your answer.)

Q: Let P3 be the vector space of polynomial functions of degree less than or equal to 3 over the field…

A: Let P3 be the vector space of polynomial functions of degree less than or equal to 3 over the field…

Q: Show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

A: We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v…

Q: Let f(x) = −4, g(x) = -5x+7 and h(x) = - -2x29x+9. Consider the inner product (p,q) = p(-1)g(-1) +…

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Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: Show that λis a root of char(x) if and only if there exosts a non-zero vector v in V with L(v)=λv

A: Assume that λ is a root of charL(x) then | λIdv–L | = 0. It is known that, the system of Bx = 0 has…

Q: If the percent decrease is 25%, what is the common ratio?

A: Common Ratio The common ratio is defined as the amount between each number in a geometric sequence.…

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

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Q: Let T: P₂ P₂ be a mapping defined by T(a + a₁x + a₂x²) = ao + a₁ (x + 1) + a₂(x + 1)². a) Determine…

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Q: True/False: If A is diagonalizable, then so is AT.

A: A matrix is said to be diagonalizable if a matrix of n×n elements has n linear independent eigen…

Q: Find w, where w3 = 1 + i. i? = -1.

A:

Q: Determine whether the following set of polynomials is linearly independent (1 – t)?, t – 2t2 + t³,…

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Q: True or False: (p, q) = p(1)q(1)+p(2)q(2) +p(3)q(3) defines an inner product on P2(R).

A:

Q: The space P2₂ represents all 2nd degree or less polynomials. A polynomial such as p(x) = 9+8z +…

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Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: Let f(x)=-4, g(x) = -5x+7 and h(x) = -2x²-9x + 9. Consider the inner product (p,q) = p(-1)q(−1) +…

A: Step 1:Step 2: Step 3: Step 4:

Q: 1. Given vectors B = (1,–2,3,0),C =(-2,1,0,4) in R*. (a) Examine if vector X = (-4,-1,6,12) is in…

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

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: Let X₁ = [1 3 −1 1]²‚×₂ = [3 −1 3 1]′, and x3 = [-1 2 −3 1]. Is b = T an element of span{X₁, X₂,…

A: No, we can write it.