Problem 33. Suppose U is the subspace of R“ defined by U = span((1, 2, 3, –4), (–5, 4, 3, 2)). Find an orthonormal basis of U and an orthonormal basis of U-.

Q: If {e, xe", e2 is a basis of solutions of y" + ay" + by + cy = 0, %3D then a =

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Q: Which of the following are a basis for the orthogonal complement of the span of (1,-2, -5, 1)7 and…

A: NOTE: Refresh your page if you can't see any equations. . write both vectors in the matrix

Q: 1)Let W CR³ be the subspace generated by the vectors (1, 0, 1)and(1, 1, 0). a )Find the orthogonal…

A: Given W⊂R3 be the subspace generated by the vectors (1,0,1) and (1,1,0). Solution a: Since every…

Q: 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x²,1 + x + 4x²,1 – 7x

A: Consider the polynomials: 1-3x+x2, 1+x+4x2, 1-7x To show that the following polynomials form a basis…

Q: The vectors ū1 (2, –3,0), ūz = (1,4, 1), ūz (2, 8, 2), ū4 (1,0, 0) and üs (3, -5, 2) span R² (you…

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Q: (- _-----«s) If {ƒ1, ..., fn} is an orthogonal basis of R¹ and U = span{f₁,..., fm}, show that U =…

A: We will be proving the statement using basic definitions of Orthogonal Basis of Rn .

Q: The vectors ₁ = (2, -3,1), u₂ (1,4,-2), uz = (-8, 12, -4), U4 = (1,37,-17), and u5 = (-3, -5, 8)…

A: We are given five vectors in R3. Out of these we have to find a subset that form the basis of R3.the…

Q: If {a, x} is a basis of solutions of x?y" + axy' + by = 0, then a = (А) —2 (В) 2 (C) -3 (D) 3 (E)…

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Q: 4. Find a basis of each vector space below and hence write down the dimension of the space. You do…

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Q: 3- Let {u,v,w} be a basis for a vector space V. Is {u + v,u + w,v + w} a basis for V?

A: Solution

Q: Let s = {(1,3, 5), (3, 3, 2), (-1, 1, 8)} be a basis for R. If u = (7, 13, 22), then (u), = %3D A)…

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Q: O that B = 3 U₂₁ U₂ ) is an orthonormal basis t U2 V. If x is a vector in v with uz •X == Suppose…

A: Orthonormal basis for the vector space V.We know any vector x in V can be written as

Q: 9) please be clear with your answer, thanks!

A: Given the coordinate matrix of x relative to a (nonstandard) basis B for Rn, find the coordinate…

Q: 1. In the {li), j), Ik)} representation, the normalized basis vectors are chosen as li) = (1). 1) =…

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Q: Is the following set of vectors S = {v,, V2. V3} basis for R³ space? Where, a. v = (3,1,–4), v2 =…

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Q: Suppose that B = {₁, 2} is an orthonormal basis for the vector space V. If x is a vector in V with u…

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Q: 19. Prove that the set {(1, 0, 0), (1, 1, 0), (1, 1, 1), (0, 1, 0)} spans the vector R' (R) but is…

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Q: 2. Apply the Gramm-Schmidt orthogonalization process to the vectors [1, 3, 2] and [1, 0, 1] in order…

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Q: 2. A 2D-subspace (manifold) in 3D- space is defined by the two vectors d;=é,+ê,-2êzand ā,=ê,+2êz-3ê,…

A: A 2D-subspace (manifold) in 3D - space is defined by the two vectors a→1=e^1+e^2-2e^3 and…

Q: et {u₁, U₂, u3} be a basis for a vector space W, where U₁ || 1 , U₂ 1 , U3 1 0 By using the…

A: are the basis of vector space W.We have to find the orthogonal basis for W.

Q: 30. Let S = {v1, V2, . .., V,} be a set of non-zero vectors in a vector space V and W = span S.…

A: See the detailed solution below.

Q: Question (1) Given a vector space V with dim V = n, along with a spanning set S = {v1,... , vk} for…

A: We will use the concept of linear independence of basis vectors.

Q: 10. Let (1,2,3) be a solution for the vector equation ru + yv + zw = 0 and consider the matrix…

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Q: Dim (3) Ex. consider T: IR ³ -> R² T( 9₁, 92, ₁₁, 95) = (artastas, 92-94)}. T NCT) = ((a., 92, 93,…

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Q: 1-Determine if W is a subspace of Mnn CEMnn, W = {AEMnn : CA'C²= A} %3D

A: It is given that W=A∈Mnn : CAtC-1=A, where At is the transpose of the matrix A. We have To determine…

Q: If {x, a} is a basis of solutions of a?y" + axy' + by = 0, then a = (A) -2 (в) 2 (C) -3 (D) 3 (E)…

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Q: Let wi = w2 = and set B = (w1,w2). Then B is a basis of R². (C 9). If T : R? → R² has matrix with…

A: We have to find first general formula for T the the sum of the coefficient

Q: Let v1 = (1,2,1), v2 = (2,9,0), v3 = (3,3,4) . Show first that S= {v1, v2, v3} is a basis for ℝ^3.…

A: A linear map is a mapping A to B between two vector spaces that preserves the operations of vector…

Q: V has bases B = (v1, v2, v3) and B' = (w1,w2, W3). If wi vị + 2v2 + 4v3, wz = 2v1 + 5v2 + 6v3, wz =…

A: Given that, B=(v1,v2,v3),B'=(w1,w2,w3) Given that,…

Q: 9. Consider the orthonormal basis S for R³ S = (v₁,v₂,v,} where v₁ = (0,1,0) and v₁ = Let u = V₂ = =…

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Q: Let V = R²x2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) = 15 - || =…

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Q: 4. Let { u1, Uz, U3, U4, U5} be an orthogonal basis for R$, y a vector in R$ , W1 = Span { u, uz}…

A: Given, {u1,u2,u3,u4,u5} be an orthogonal basis for R5,y a vector in R5,  W1=Span{u1,u2}   and…

Q: 15. Assume that the vector space R³ has the Euclidean inner product. Apply the Gram-Schmidt process…

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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.