linear algebra
posted by chris .
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.
Respond to this Question
Similar Questions

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 … 
Algebra
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) … 
math
Find an orthonormal basis for the subspace of R^3 consisting of all vectors(a, b, c) such that a+b+c = 0. The subspace is twodimensional, so you can solve the problem by finding one vector that satisfies the equation and then by constructing … 
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? 
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 … 
Linear Algebra
Prove that If a vector space is of dimension n and a set of vectors spans V, then that set of vectors must be linearly independent. 
Linear Algebra
Vector in SpaceDirections and Magnitudes Let a, b, c, d, e, & f be vectors such that <a,b>=6, <a,c>=6, <a,c>=4, <b,c>=7, b+c=d, 8a+8b=e, 4b+2c+f compute the following inner product: <b,a>=__ <a,d>=__ … 
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 … 
math vectors
Use a specific example to prove that the cross product is also not associative. That is, use three specific vectors in 3space to show that Vector a×(Vector b × Vector c) is not equal to (Vector a × Vector b) × Vector c. Can you … 
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.