Recent content by Jaglowsd

Much appreciated for the help from the both of you.

Since AX=B does not satisfy 3 because if X=0 then B must be a zero vector then it is not a vector space. Am I correct?

1) Vector addition of vectors u,v 2) Scalar multiplication of a real number a, and u 3) A vector space has to have a zero vector

Sorry, I am still trying to wrap my head around vector spaces. Could you elaborate why X=0 must solve the system to be a vector space.

So unless B is a zero vector than in any case AX=B can not be a vector space? It must be AX=0, or the null space?

Let B be a non-zero mx1 matrix, and let A be an mxn matrix. Show that the set of solutions to the system AX=B is not a vector space. I am thinking that I need to show that the solution is not consistent. In order to do so would I need to show that B is not in the column space of A?

Good evening everyone, I hope everyone is having a better evening than myself thanks to this homework problem. Let P be the set of positive numbers. For a,b in P, define a+b=a x b; for a in P and a real number r, define r x a= a^r. Show that P is a vector space using ⊕ as addition and (circle...