Let V is finite vector space and suppose that V=internal direct sum of U and S1. Also V=internal direct sum of U and S2. What can you say about the relationship between S1and S2? What can you say if S1 is a subset of S2?

Q: There was no information/work on if V is a vector space

A:

Q: Is it possible to make Z into a vector space if we redefine addition?

A: To check: the possibility to make ℤ into a vector space.

Q: Prove that M2,3 is a vector space

A: To prove that M2,3, the set of 2 by 3 matrices, is a vector space, we need to show that it satisfies…

Q: How do you extened an independent set to a basis?

A: Thanks for the question :)And your upvote will be really appreciable ;) To understand this problem,…

Q: A student learning about linear independence makes the following inaccurate statement: "A subset S…

A: We have to solve given problem:

Q: Determine if each of the following sets with the indicated operations of addition and scalar…

A:

Q: Suppose ₁, 2, 3 is an orthogonal set of vectors in R³. Let w be a vector in Span(V₁, V2, V3) such…

A: Given: v1, v2, v3 is an orthogonal set of vectors in ℝ5.           v1·v1=30, v2·v2=25.25, v3·v3=9…

Q: Let A = -2 -2 5 5 -5 -2 Give a non-zero vector in the null space of A. -5 -2 -1 5 5 1 2

A:

Q: vector

A: (a+b)(v+w) = (a+b)v + (a+b)w

Q: 3) For each set of vectors below, determine if the set is dependent or in- dependent. If the set is…

A: We will first check the linearly independence of this set of three vectors

Q: Compute u – 3v, u v and u x w.

A:

Q: = If w₁, W2, W3 are independent vectors, are the sums V₁ = W2+W3 and V₂ W₁ +W2 independent or…

A:

Q: 5. Complete the proof of the property below by supplying the justification for each step. Let V be a…

A:

Q: Let V be the set of all positive real numbers Determine whether V is a vector space with the given…

A:

Q: 1) Suppose v1, V2, V3, V4 span a vector space V. Prove that the list vi - v2, V2 – V3, V3 – V4, V4…

A: Spanning set of the vector space

Q: 1.W.4 We'll work inside the vector space of polynomials in degree < 2, which is denoted P<2. Let P1…

A:

Q: 25. Consider the following elements of the polynomial vector space. Are they linearly independent?…

A:

Q: 5. Let S be the set of all points (x11, X12, X13, X22, x23; X33) E K® such that the matrix x11 *12…

A: The objective is to determine if the set S is convex or not, where  S is set of all points…

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.