Let W = {(a,b, c, d)| a – 5 b = 0 } be a subspace of R*. Then a basis for W is O (5,1,0,0).(0,0,1,0),(0,0,0,1)} O (1,5,0,0)} O (1,5,0,0).(0,0,0,1)} O {(1,5,0,0).(0,0,1,0).(0,0,0,1)}

Q: S- ((2, 5, -3, -5), (-2, -3, 2, -2), (1, 3, -2, 5), (-1, -5, 3, 2)} 00

A: Given that S=2, 5,-3,-5, -2,-3, 2,-2, 1, 3,-2, 5, -1,-5, 3, 2. The objective is to find a basis for…

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Q: 11. Find a basis of the following subspace of R4. all vectors of the form (a, b, c, d) where a + b –…

A: The solution is given as

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: 4. Find an orthogonal basis of the subspace W of R5 spanned by {ū₁ = (1, 1, 1, 0, 1), 2 = (1, 0, 0,…

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Q: 11. Find a basis of the following subspace of R4. W = all vectors of the form (a, b, c, d) where a +…

A: To find: Basis of W={(a,b,c,d) | a+b-c+d=0}.

Q: Let W = {(a,b,c, d) : a+2b= e, d= 3a} be a subspace of R', then one of the following is a basis for…

A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :   { (…

Q: - (-, s) Find a basis for the subspace W C R', consisting of all the vectors orthogonal to the…

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Q: Consider the subspace S of the Euclidean inner product space R* spanned by the vectors v₁=(1,1,1,1),…

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Q: 9. Let S be the subspace of R3 generated by the vectors (1, – 1,0), and (2,3, 1). Let T be the…

A: This question is related to Linear Algebra

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: Let W be a subspace of R4 spanned by the set Q = {(1, 1, 3, 1), (1, 2,−1, 1), (1, 1, 0, -1)}. (i)…

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Q: Let V be the subspace of R' spanned by the vectors below: u = (1,2, 1,3,2), Uz = (1,3, 3,5, 3), Uz =…

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Q: a) {(1,-1,2),(5,-4,1),(7,-5,-4)}. b) {(1,3,3),(1,5,-1),(2,7,4),(1,4,1)}.

A: To Determine a basis for the subspace of Rn spanned by the given set of vectors by usingthe concept…

Q: Let W be the subspace of R³ spanned by the vectors =(1,2,3,-1.2) and v= (2,4.7.2.-1). A basis of the…

A: Let W be a subspace of a vector space V. Then orthogonal complement of W is defined as, W⊥={u| v∈W…

Q: Which of the following is a basis for the subspace {:) X y z x = y+z and x, y,z €RC M2x3(R) ? 0 x 0…

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Q: Let W be the subspace of RS spanned by the vectors = (1,2,3,-1,2) and v= (2,4,7,2,-1). A basis of…

A: We have to solve given problem:

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

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Q: a) Give an example of subspaces U = span(f1, f2, f3) and V = span(g1,92; g3) of RaJa] such that…

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Q: 6. Let V = R³ and F = R. Let W = { (a, b, c) | a+b-2c=0 where a, b, c are in R} It can be shown that…

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Q: Let W = {(a, b, c, d) : a + 2b = c, d= 3a} be a subspace of R', then one of the following is a basis…

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Q: Advanced Math Question

A: First we need to arrange given data in equation form- Where  Ans (a) X= number of slugs of type A Y=…

Q: Consider the subspace S of the space Euclidean inner product (1.1.1.1), ₂(1.1.2.4). v,= (1.2,-4,-3).…

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Q: Let W be the subspace of R5 spanned by the vectors = (1,2,3,1,2) and v= (2,4,7,2, -1). A basis of…

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Q: #6. Let W be the subspace of R³ spanned by the two vectors (1, – 1,1) and (3, – 2,0). Which one of…

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Q: Let W = {(a, b,c,d)| 5a - b = 0} bẻ a subspace of R'. Then a basis for W is %3D ((1,5,0,0)} O…

A: option b is correct answer . below is the explanation

Q: Let W = {(a, b, c, d)| 5a – c = 0 } be a subspace of R. Then a basis for W is O…

A: We find basis of W subspace of R^4

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

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Q: (11) Find a basis for the orthogonal complement of the subspace of R" spanned by the vectors V1 =…

A: We have to solve given problem;

Q: 3. Let W = ((1,2,3,6), (4,–1,3,6), (5, 1, 6, 12)) %3D W2 = ((1,-1,1,1), (2,-1,4, 5)) %3D be…

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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.…

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Q: Q 3: a) i. Show that W is a subspace of R*. ii. Find a basis for W. Let W = ((a +c, a + b + 2c, a +…

A: According to the policy we are allowed to do only one question with their sub-parts (If any). So I…

Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 1, 0),…

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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.