Recent content by cocobobos

So if a vector y in is Nul(A) then this means that the equation y=c1v1+...+cnvn with cn scalars must equal 0?

Ohh ok do you mean that if Ax is in the null space then: Nul(A) must contain the zero vector If x ∈ Nul(A) and y ∈ Nul(A), then x + y ∈ Nul(A) (aka closed under addition) If x ∈ Nul(A) and c is a scalar, then cx ∈ Nul(A) (aka closed under scalar multiplication)

So Ax must equal 0?

Just say that P^3 is isomorphic to R^4 and then convert those vectors into a corresponding matrix and row reduce and your pivotal columns will tell you what vectors are linearly independent.

So for a 10x10 matrix the null space of that matrix would consist of all vectors x in R^10 such that Ax=0 ?

Well if Ax is in Nul(A) then isn't the null space of A the same as the solution set to the homogeneous system Ax=0?

Ok so the column space of A consists of all possible products Ax for any x an element of R^n. So if the Col(A) is equal to the Nul(A) which is the set of all vectors x for which Ax = 0 then this tells us that Ax must be equal to zero? aka the linear combination must be equal to 0?

So what we can say about Ax is that it will be a linear combination of the column vectors of A?

I'm really confused what do you mean by A^2? Are you saying that A is the identity matrix? I guess I'm just confused in general about WHEN the column is EVEN equal to the null space at all.. How can you tell?

Homework Statement Find all 10x10 Matrices such that the column space is equal to the null space. Homework Equations Choose Function: n!/k!(n-k)! where n is the total number of elements and k is the number k-cominations of the set. rankA+dimNulA=n for a matrix in R^n The...