Let U and W be subspaces of Vector space V. Answer the following questions. Argue your answers: 1. Is the intersection of U and W a subspace of V? 2. is the union of U and W a subspace of V? 3. The sum of the subspaces U and W are defined as follows: U + W = {u + w: u belongs to U, w belongs to W} Show that U + W is a subspace of V.

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: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z = 0 y? + 3 x = 3 z Explain…

A: The solution is given as

Q: et S be the subspace of IR° spanned by u and v. Find the closest vector p in S to the vector w. -2 7…

A: In this question, concept of basis is applied. Basis A basis for a vector space V is a collection of…

Q: . Let V be a vector space, and {v1, ··· , vn} be a set of vectors that spans V . Show that the set…

A:

Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. 3 - 1 y = 0 V₁ = 1 16 1 - 4 - 1…

A:

Q: Find the closest point to y in the subspace W spanned by v₁ and v2. y= 3 -1 1 16 V1 11 1 -4 1 5 V2 =…

A:

Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

Q: Let H be the set of all points in the third quadrant in the plane V = R². That is, H = {(x, y) | x <…

A:

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

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Q: 1. Let "W" be the set of vectors of the form below. Show that "W" is a subspace of R4. You must show…

A: To show whether W is the subspace or not.

Q: Find all values of h such that vector y will be in the subspace of R spanned by vectors 3. V1, V2,…

A: we will first find the equivalent matrix and then reduce it to row echelon form

Q: Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector…

A:

Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y = 5 - 1 1 18 V₁ 1 - 2 - 1 3 V2…

A:

Q: 2. Let W be the set of all vectors in R? whose first component is 2. Is W a subspace of R2? Justify…

A: It is not a subspace.

Q: Show that if V is a real vector space and av=0, then a=0 or v=0

A:

Q: Let W be the subspace spanned by u, and u₂, and write y as the sum of a vector in W and a vector…

A:

Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y = 13 The closest point to y in…

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Q: Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector…

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Q: Determine: if W = the set of all vectors in R2 whose components are integers is a subspace.

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Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

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Q: If V is a vector space then show that cV=V.

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Q: The vector x is in a subspace H with a basis B = {b, ,b2}. Find the B-coordinate vector of x. - 1 8…

A: Let β={ u1  ,u2  , ......., un } be an ordered basis for a finite dimensional vector space V then…

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.