Find a basis {p(r), q(z)} for the vector space {f(z) € P3[r] |f'(3) = f(1)} where P3 [a] is the vector space of polynomials in z with degree less than 3. p(z) = •q(z) = %3!

Q: Let 8 = {1, x, ex, xe*} be a basis for a subspace W of the space of continuous functions, and let Dy…

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Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the…

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Q: 1. If T is a normal operator on a finite dimensional inner product space V and if W is a subspace of…

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A: Here we have to find an orthonormal basis for the subspace spanned by 1, x, x2:

Q: 個同 . Find a basis for the Subspace W of R spanned by S What is the dimension of W?

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Q: Let {u1 (x) = -9, u2 (x) = –12x, Uz3 (x) = –12x²} be a basis for a subspace of P2. Use the Gram-…

A: we have goven basis of P2B=u,(x)=-9,u2(x)=-12x,u3(x)=-12x2f,g∫01f(x) g9x0dx   on c[0.1]According to…

Q: f(x) = 9, g(x) = 7x – 4 and h(x) = -2x². Consider the inner product (p, q) = / p(z)q(x) dæ in the…

A: Let S={v1,v2,v3} represent the orthonormal basis for the subspace. By Gram Schmidt Process,…

Q: Give an example of a non-zero subspace of R^4 which has dimension &gt; 1 and does not contain any of…

A: Consider the example f(x) = {2 + x + x2}, this given polynomial has dimension 3 with the basis {1,…

Q: If V is the vector space of real valued continuous functions , then show that the set W of all d’y…

A: Our Aim is to show that the set W of all solutions of the differential equation3d2ydx2-5dydx+7y=0…

Q: If I is a normal operator on a finite dimensional inner product space V and if W is a subspace of V…

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Q: Find an orthonormal basis for the subspace of Euclidean 3-space below. W = {(x1, x2, x3): x1 + x2 +…

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Q: Is W a subspace of the vector space? W is the set of all matrices in M, with zero determinants. n,n…

A: Use subspace test if u and v in W them au+v must be in W where a is any scalar

Q: Let B = {1, x, eX, xe*} be a basis for a subspace W of the space of continuous functions, and let Dx…

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Q: If W is a subspace of R" of dimension k with a basis {v1,e,2,..., v%} then W Range(|v1 v2 vn)). ...…

A: Given: Let W be a subspace of Rn and dimk=k Let B be a basis of k then B=k Also B is a linearly…

Q: Find an orthogonal basis for the subspace {(x, y, z) E R³ | x + 4y – 2z = 0} -

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Q: In the vector space of functions f: R → R, find a basis for the subspace spanned by {sin t, sin 2t ,…

A: Solving question by theorem vector space

Q: If T is a normal operator on a finite dimensional inner product space V and if W is a subspace of V…

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Q: F,[x] is the vector space of all polynomials over a field F of degree at most n and has a standard…

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Q: 26. In the vector space of all real-valued functions, find a basis for the subspace spanned by {sin…

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Q: (3) Suppose that V is a finite dimensional vector space over R and T € L(V) has no eigenvalues.…

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Q: Find a basis for the subspace of R, the plane 2x +y-z+ 3w-0 and convert it into an orthonormal ban

A: Given the subspace 2x+y-z+3w=0. To get the orthonormal basis. The formula for orthonormal basis is,…

Q: Let be the vector space of polynomials of degree less than or equal to one with real coefficients…

A: The given vector space is the set of all polynomials of degree less than or equal to one with real…

Q: Let f(x) = 6, g(x)= 8x + 7 and h(x) = -3x² + 2x + 4. Consider the inner product (p, q) = p(-1)q(-1)+…

A: A

Q: Let L be a linear operaton on a vector space V. Let A = vith respect to a basis B = {v1,., Vn} of V.…

A: Let, L be linear operator on the vector space V. Let, A be the matrix representing L with respect to…

Q: {[:} 5. (a) Consider the subspace W = span and consider the vector -1 1 u = -1 |. Find the vector w…

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Q: Find an orthonormal basis for the subspace of C(R) generated by the functions {1, x, x²} with…

A: W e find an orthonormal basis for the subspace of C([0, 1]) generated by the function (1, x, x^2)

Q: 4. Find an orthonormal basis for W+, where W is the subspace of R' spanned by the vectors (-1,…

A: To find- Find an orthonormal basis for W⊥, where W is the subspace of ℝ4 spanned by the vectors -1,…

Q: 4. Let be B = {1,eª, xe²} a basis of a subspace E of the space of continuous functions, and let D.…

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Q: . Find a basis for the vector space T, and state its dimension: T = Intersection of the plane 3x -…

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Q: Let V be the subspace of C[a, b] spanned by1, ex, e−x, and let D be the differentiation operatoron…

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Q: 1. Consider the vector space V = M3x3(C) over the field R. Let U be the subspace of V consisting of…

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Q: Find a basis for the subspace W of R spanned by 3 7 2 2 10 6. 7 4 What is the dimension of W?

A: Given vectors, 122, 321, 11107, 764

Q: Let f(x) = 4, g(x) = 4x + 6 and h(x) = 2x². Consider the inner product (p, q) = p(x)q(x) dz in the…

A: The given question can be solved as shown in step2.

Q: Consider the inner product space G-1.1) with inner product: -f()g()dz f(x)g(x)dx %3D V6 Let U= x…

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Q: 2. Find a basis for the subspace W = {[r y z]T: ax + by + cz = 0, a, b, c e R} of R". What is the…

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Q: 3) Find a basis for the subspace of R that consists of the intersection of the planes X-3Y = 5Z and…

A: This is a problem of vector space.

Q: The vectors v1 = (0, 1, 0) and v2 = (1, 1, 1) span a plane in R3. Find an orthonormal basis for this…

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Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the…

A: Given that V be the vector space of polynomials of degree ≤2 with real coefficient, endowed with the…

Q: let P5 be the standard vector space for polynomials of degree <=5 and U be of the set of all…

A: Let P5(x) be the standard vector space for polynomials of degree≤5. and U be the set of all…

Q: Let {u1 (x) = 12, u2 (x) = 12x, u3 (x) = 8x² } be a basis for a subspace of P2. Use the Gram-Schmidt…

A: Orthogonal basis, therefore inner product will be zero for distinct two elements.

Q: Apply the Gram-Schmidt orthogonalization process to find an orthonormal basis for 0. the subspace U…

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Q: a) T: M, → R, where M, is the vector space of n by n matrices over a field, and T (A) = det(A). b)…

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Q: In the vector space f, of polynomials of degree at most two, the third column of the matrix of…

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Q: Consider the vector space P3 of polynomials of degree at most 3 together with the zero polynomial..…

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Q: a) T: M, → R, where M,n is the vector space of n by n matrices over a field, and T (A) = det(A). b)…

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A: We will find out the required solution.

Q: Find a basis {p(x), q(x)} for the vector space {f(x) E P2[x] | f' (9) = f(1)} where P2[x] is the…

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Q: Let B = {1, x, ex, xex} be a basis for a subspace W of the space of continuous functions, and let Dx…

A: Given: B=1, x, ex, x ex is a basis g=for a subspace W of the space of continuous functions. DX is…

Q: Let {u1 (x) = -9, u2 (x) = 18x, uz (x) = –12x²} be a basis for a subspace of P2. Use the Gram- %3D 1…

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Q: The cosine space F3 contains all combinations y(x) = A cos x+ B cos 2x+C cos 3x. Find a basis for…

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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.