Let V = Poly4(R) and let B = (1, x2 − 1, x, x^3 − 2x, x^4 − 3x^2 + 1). (a) Find a basis C of V such that every polynomial in C has degree 4; find the matrix[D]B←C of the derivative map D : V → V ;(b) Find the dual basis to B. Your answer should be expressed in terms of differentialoperators with polynomial coefficients.

Q: Find an orthonormal basis of ℋ:  x− 2y − 3z = 0.

A: Introduction: The Gram–Schmidt process is a method for orthonormalizing a set of vectors in an inner…

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Q: a) Let D be the differential operator on the vector space P2(R). Given two ordered bases a = (1, x.…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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Q: 9. Find a basis y1 (x), y2(x) of the space of solutions to y" = y such that Y1 (0) = 1, y (0) = 0,…

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Q: 2. Find the matrix of the reflection operator with respect to the plane x+y =0 (in the basis i, j.…

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. -3° 2 , 83 = S2 1

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Q: 6. Find the standard matrix for the operator in R2 for a rotation about the origin by °45 and then…

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Q: This is a textbook question, not a graded question   The first four Hermite polynomials of the…

A: We  have to find the basis for P3

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A: Given v1=12-2,v2=00-1,v3=010. Find the orthogonal basis x1,x2,x3 using the gram schmidth.

Q: Consider the linear transformationT : R² → R´which consists of rotation counterclockwise by 90°…

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Q: (10) R¹3x+2y-20). Determine an orthonormal basis of W

A: Given : W={x,y,z∈R3:3x+2y-z=0}

Q: Consider the operator T E L(C) whose matrix in the standard basis of C' is (4 0 -6) 3 2 8 10 -1, a)…

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Q: (a) Prove that the set ẞ = {p0(x), p1 (x), ... , Pn(x)} of Lagrange polynomials is linearly…

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Q: 15. Use the Gram-Schmidt process to transform the basis {r1, x2, a3, T4} into an orthogonal basis…

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Q: 2. Consider the quadratic form Q : R° → R, where Q(x1, 22, x3) = –2x – 8x – 18x3+ 8x1x2 + 4x1x3 +…

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Q: Suppose that you have three vectors: f1 (x) = 1, f2 (x) = x – 1, and f3 (x) = ; (x² – 4x + 2), that…

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Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". {G ) (-) 0, 0, 1)} x =…

A: Given vector is x=20, 10, 25 and the corresponding orthogonal basis is B=35, 45, 0, -45, 35, 0, (0,…

Q: 5. Find the standard matrix for the linear operator T: R³ R³ that first transform by the formula…

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Q: Consider an inner product on two P3 vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2):…

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Q: The Hermite polynomials form an orthogonal (not orthonormal) basis with this inner product: (Hm[Hn)…

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Q: Consider the linear operator T on the vector space R2[x] given by T(a+bx+cx2) =…

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A: Orthogonal set problem....

Q: The Gram-Schmidt process transforms the basis u1=(-1, 2), uz=(6, –2) of R into the orthogonal basis…

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Q: Find a 3 x 3 matrix A (with real number entries) whose characteristic polynomial is det(A – rls): *…

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Q: Given that x, = – 1 and x1= 1. Then the basis of the first Lagrange polynomial Lo(x) and L,(x) are…

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Q: The Gram-Schmidt process transforms the basis u=(-1,3), u2-(7,-1) of R into the orthogonal basis…

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Q: 6. Define fe (R2)* by f(x, y) 2x + y and T: R2 (3x + 2y, x). (a) Compute T'(f). (b) Compute [T']p,…

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Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". x = (10, 20, 5), B =…

A: We will use the definition of inner product and Orthonormality of B

Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". {(금, 승 이) (-승름이 (0,0, 1}…

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Q: Use the Gram-Schmidt process to find an orthonormal basis for im(A), where 2 1] 1 1 -2 0

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Q: Given that xo= -1 and x1= 1. Then the basis of the first Lagrange polynomial Lo(x) and L,(x) are…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: → 5. Find the standard matrix for the linear operator T: R³ R³ that first transform by the formula…

A: given formula Tx,y,z=2x-y+z, -x+2y+z , x-z where T:ℝ3→ℝ3 standard basis for ℝ3 are 1,0,0 , 0,1,0…

Q: Let P2 be the polynomials of degree no more than 2. Is {x2+x+1,2x+1,3x2+1} a basis for P2 ?

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Q: After applying the Gram-Schmidt Orthonormalization Process to the basis B a 1 we get the basis B'…

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Q: 3. (а) Find an orthonormal basis B = {ū1, ū2, ū3} of R³ such that ủi and the x-component of ūz is…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.