Let Wi and W2 be two two-dimensional subspaces of the linear space R³, that is dim W1 W = W1n W2 is a subspace of the dimension at least 1, that is dim W > 1. dim W2 = 2. Prove that the intersection of these two-dimensional spaces

Q: Let Y be a vector subspace of a normed space X. Show that the closure of Y is also a vector…

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Q: If V3(R) is a vector space and W₁ = {(a,0, c): a, c = R} and W₂ = {(0,b,c): b, c = R} are two…

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Given W be a subspace spanned by the u's, We have to write y as the sum of a vector in W and a…

Q: 6. Let Vi and V2 be subspaces of R" such that Vi C V2. Show that any vector v E R" can be uniquely…

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Q: 12): x € R. Is W a subspace of V? Expalin your 3x- Q1. Let V = R³ and W = answer? Q2. Show that M2x2…

A: The properties of subspaces: Closed under multiplication; Closed under addition; Contains the…

Q: Let W be a subspace of a vector space V. Show that if x is in both W and W+, then x = 0.

A: Solution is given below

Q: a. The union of two subspaces of a vector space is always a subspace. b. The basis for the zero…

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Q: Let S be a subspace of R" and let S be its orthogonal complement. Prove that S- is also a subspace…

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Q: . Consider M₂ (R) as a vector space and its subspaces U₁= {A € M₂(R): A¹ = A} and U₂ = {A € M₂(R) :…

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Q: Let U be a subspace of a finite-dimensional Prove that dim(U) = dim(V) if and only if U = V. vector…

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Q: If we know that W is a subset of the vector space V and we know that W contains the zero vector 0,…

A: This statement is False.  By using property of subspace we can prove this statement is False.

Q: Suppose U and W are subspaces of a vector space V. Prove that if U C W, then U + W = W.

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Q: Let U1, U2 and W be the subspaces of a vector space V. Prove or give a counter example if V = U1 ⊕ W…

A: U1,U2 and W be the subspaces of a vector space V.

Q: Suppose that V is finite dimensional and U is a subspace of V such that dim U = dim V . Prove that U…

A: Given that V is a finite dimensional vector space and U is subspace of V such that dimU=dimV. Let…

Q: If V is infinite-dimensional and S-is an infinite-dimensional subspace, must the dimension of V/S be…

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Q: Show that the set W={(x,y,1)|x and y are real} is not subspace of R3.

A:

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.