[Linear Algebra] Space, null space, dimension?

Well in my answer I will note the nullspace N(A) by taking the international notation : Ker(A) it 's the same! ;-) here we go : the source space E is a 4D space, say R^4 first we see that for u1 = t (t for transpose in column!) : A*u1 = O_vector of R^2 therefore : u1 € Ker(A) let you (x) (y) (z) (t) be any vector of E then x € Ker(A) the null space of A iif : Au = O_vector of R^2 (target space ha 2D!) this gives us 2 scalar equations : 0x -2y + 2z - 6t = 0 (1) 0x + y - z + 3t = 0 (2) and we see that both equations are equivalent : (1) = -2 * (2) means one equation is enough!

It is the set of vectors that yield the 0 matrix (i.e. , A*B = 0) where B consists of the desired column vectors. Set up the matrix multiplication for A * {b11, b12, b13, b14} and A*(b21, b22, b23, b24} Choose b11, ... b24 such that the resulting matrix is 0.

This is just algebra.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.