Find an orthonormal basis for the subspace of C(R) generated by the functions {1, x, x²} with respect to the inner product (f, g) = So S()g(1) dt.

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 1 1 V1 = V2 1 and let H = span{v1,V2} be a subspace of R* Find an orthonormal basis for H.

A: We will use Gram-Schmidt process to form the orthonormal basis of H. According to uk=vk−∑i=1k−1…

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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: Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R spanned by V1 = (1,…

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Q: Find a basis for the given subspace of R° , and state its dimension for the plane 4 x - 2 y + 5 z =…

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Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 -1 -1 projw (7) = %3|

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Q: Let {x1, x2, . . . , xk, xk+1, . . . , xn} be an orthonormal basis for an inner product space V. Let…

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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 > 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: 4 Let S be the subspace of R* spanned by x1 = (1,0, – 2, 1)" and x2 Find a basis for S. (0, 1, 3,…

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Q: 1 Q5. Find an orthonormal basis of the subspace spanned by the vectors

A: The solution is given as

Q: 2 Find the orthogonal projection of u = 1 onto the subspace of R3 spanned by the vectors -3 - 2 V1 =…

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Q: Use the Gram–Schmidt process to find an orthonormal basis for the subspace of R4 spanned by x1 =…

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

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Q: Q5. Find an orthonormal basis of the subspace spanned by the vectors 1 3 3 121C

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Q: For a certain subspace W, the orthogonal projection of the vector y = 3 onto W is ŷ 2. Use this…

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Q: Find an orthogonal basis for the subspace H of IR that is spanned by the vectors 1 1 1 -2 1 V1 = V2…

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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: at | f = a is a subspace of RI0,1] if and

A: Two step test

Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 1 -1 1 -1 1 1 1 [1] 1 II…

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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: Let and y Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R'…

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Q: Let S be a subspace of V. Starting with a basis {81,..., s} for S, how would you find a basis for…

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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: if a vector space is the set of real valued continuous functions over R , then show that the set W…

A: Given V is a vector space of all continuous functions over ℝ. W is a set of differential equation…

Q: W= {x: where x are eigenvectors of an A} Is W a subspace of R" ? Show the prove

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Q: Suppose {x,y} is a basis for a subspace W of Rn. Let u = x + y and v = x − y. Show that {u,v} is…

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Q: Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R3 spanned by v1 = (1,…

A: See solution below

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 of the subspace of R defined by the equation 6y, + 3y, – 4y, = 0 Basis:

A: Given data÷

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: 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 H be the subspace of R with basis B -2 and let x 6. (:) Is x a vector in H? 9. If x is in H,…

A: Given basis is B

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: Find an orthonormal basis for the subspace of R generated by the following vectors: (a) (1,1, –1)…

A: We have given the following vectors: a) (1,1,-1) and (1,0,1) b) (2,1,1) and (1,3,-1) We have to find…

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 x = -2 and y =| -3 -3 Use the Gram-Schmidt process to determine an 3 orthonormal basis for the…

A: The Gram-Schmidt process converts a set of vectors to an orthonormal basis. Consider two vectors v1→…

Q: 5. Find basis for the subspace u- of R for the vector u = orthogonal subspace of u) (1,3,-4). (Here…

A: As we know that S=v1,v2,...vk be a set of vectors in Rn  then S is called an Orthogonal if and only…

Q: Let u, = u2 = -1. and uz =0| Note that u, and uz are orthogonal but that uz is not orthogonal to…

A: Introduction: If two vectors are perpendicular to one other, they are said to be orthogonal. The dot…

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 W be the subspace of R3 with orthonormal basis {w1, w2}, where

A: Given: w1=010 w2=15025 v=12-1

Q: Find the orthogonal compliment of the subspace W of 2x2 upper triangular matrices in the vector…

A: Using standard inner product in the space of matrices.

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

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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.