Let vị 2,v2 8,and w Determine if w is in the subspace of R generated by v1 and v2.

Q: 2. Let а — lb +c а S = {[a – b ,b,c € R a a. Show that S is a subspace of M2x2. 31 -2 31 5 b. Is |…

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Q: Suppose that U and V are both subspaces of R . Prove that their intersection U ∩ V = {v : v ∈ U…

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Q: Show if W is a subspace of the vector space X, then W is convex.

A: Definition used: A set K in a vector space V is called convex if and only if  x, y belongs to K,…

Q: Determine; if W = the set of all odd functions is a subspace.

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Q: Let V₁ 1 -2 3 2 {V1, V2,V3}. V₂ = 2 -2 V3 7 8 7 - 10 and u = Is u in the subspace of R4 generated by…

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Q: Let W be the subspace spanned by the given vectors. Find a basis for W-. 1 -1 1 W1 W2 -5 -2 1

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Q: Which of the following sets W is NOT a subspace of R3? (Select all that apply.) O w= y : 3x-y+2z-1=0…

A: To identify the which of the given sets are not subspace.

Q: What is the dimension of the following subspace U of R2x2 ? 3 U = span({ }) -2 -2

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Q: Solve using separation of variables. dN 18. +N =Nte²+2 dt dy dx 19.². =y-xy, y(-1) = -1

A: 18.Given differential equation is .We have to solve the differential equation by separation of…

Q: The set of points where y = -4. The set of points where x = -5. Subspace of R2 Not a subspace of R²…

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Q: Let S be a 2D subspace of R. Find projs if projs =

A: Let S is a 2D subspace of ℝ3 projs<2,-1,1>=<0.5,0.5,1> So consider the 2-D plane given…

Q: Suppose C is a linear code (i.e. subspace), and u,v are in the same coset of C. Show u+C = v+C

A: Definition A subset C⊆V(n,q) is a linear code if1) u + v ∈ C for all u, v ∈ C2) au ∈ C for all u ∈…

Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 19, Un 28 国 26 20 -2 -26…

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Q: Is W a subspace of the vector space? If not, state why. (Select all that apply.) W is the set of all…

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Q: Determine if v is in the subspace of P3 given by span{x + x - 5, x2 + 2x + 1, x-x2 + x}. v = x? + 2x…

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Q: v1 Determine if the subset of R consisting of vectors of the form where v1 - v2+ v3 – v4 + v5- - Un…

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Q: Find a basis for the orthogonal complement In R of the subspace spanned by the vectors: and For the…

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Q: S� is a set of vectors in a vector space V�, then SpanS is a subspace of V�. Please show that this…

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Q: how that if T is a linear operator on V and W1, W2 are T-invariant subspaces of V, en W1+ W2 is a…

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Q: Let v₁ = O 1 5, V₂ = No Yes -2 -7 13 and w= - 3 -6 19 Is w is in the subspace of R³ generated by v₁…

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Q: Show that every subspace of ℝ is either {0} or ℝ.

A: Given: ℝ. To Show: Every subspace of ℝ is either {0} or ℝ.

Q: Explain why the subset а — b S = a +b а,bER -26 – 3a of R3 is or is not a subspace of R³.

A: Given subset of R3 is  S={a-ba+b-2b-3a|a,b∈R} explain if S is subspace of R3

Q: Let 5 Find a basis of the subspace of R4 consisting of all vectors perpendicular to v.

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Q: Let V=R\power{3}. Show the set    W={(a,b,c): a\power{2

A: Our claim is that given subset W of V=R3 is not a subspace of V.Where   W=(a,b,c): a2+b2+c2≤1

Q: Determine whether the statement below is true or false. Justify the answer. A subset H of R" is a…

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Q: Determine all subspaces of W.

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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.