# Algebra

posted by .

How would you prove this theorem:

The column space of an m x n matrix A is a subspace of R^m

by using this definition: A subspace of a vector space V is a subset H of V that has three properties: a) the zero vector of V is in H. b) H is closed under vector addition. c) H is closed under multiplication by scalars.

## Similar Questions

1. ### math

There is one step in a proof that I don't understand. Could someone please explain?
2. ### math

If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent. You know that if statement X implies statement Y then that is equivalent to Not(Y) implies Not(X). You can start by taking the column vectors …
3. ### math

Prove that if A is a symmetric n x n matrix, then A has a set of n orthonormal eigenvectors. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on the correct topic, …
4. ### linear algebra

Show that a subset W of a vector space V is a subspace of V if and only if the following condition holds: If u and v are any vectors in W and a and b are any scalars, then au + bv is in W.
5. ### Linear Algebra

V = Mnxn is a space vector formed by all the square matrices. Is W = {A in Mnxn : A^x = A} a subspace of V?
6. ### Linear Algebra

1/ Prove that the set V=R+ ( the set of all positive real numbers) is a vector space with the following nonstandard operations: for any x,y belong to R+ & for any scalar c belong to R: x O+ ( +signal into circle) y=x.y (definition …
7. ### Math Elementary Linear Algebra

determine whether or not the given set forms a basis for the indicated subspace: #1 {1,1,0), (1,1,1)} for the subspace of R^3 of all (x,y,z) such that y= x+z #2 {[1,2,-1,3), (0,0,0,0)} for the subspace of R^4 of all vectors of the …
8. ### algebra

prove that if U and W are vector subspaces of a vector V, then UV, is a vector subspace of V
9. ### Linear Algebra

W= [ a , a+b ] (2x2 matrix) [a-b , b ] a, b are element of R Show that W is a Subspace of M22?
10. ### Math

Let V and W be vector spaces and assume that T be a linear mapping from V to W. (a) Show that ker(T) is a subspace of V . (b) Show that range(T) is a subspace of W.

More Similar Questions