Recent content by Maths2468

I have a linear transformation P:z→z I want to show the Kernel (p) is a subset of the kernel (P ° P) I know that the composite function is defined by (P ° P)(x)=P(P(x)) Where do I begin with this? To find ker(P) I would do P(x)=0 but I am not sure how I would do this here. What steps...

The value of lambda I am interested in is 0. AT the end should it be T(A)=0? Is this stuff needed to answer the question?

What should it be? to calculate eigenvalue you use Ax=lambda x I know it is a relatively new topic we have started and I can not stand it. But I try

for "vector x is in the kernel of A" ker(A)={x belongs to X: T(x)=0} I am not sure about the other one. Great question by the way, really forcing me to think and understand.

what are you asking for the original matrix?

ok cool. I am starting to understand a little better. How do you know the kernel A is the same as the set of eigenvectors with eigenvalue 0? Where do I go from here?

Im sorry. I am really really bad/hopeless at linear mathematics. When I meant that A(x,y,z)=0

yes so I assume the original suggestion was bad.

I am doing maths.I find the course very well except for linear stuff. I can not picture things. Yeah if you square it you get itself again. we have only just touched on it. I am kind of going ahead of the course.

Lets say you have a linear transformation P. The eigenvalues of the matrices are 0,1 and 2. How would you show that ker P belongs to the eigenspace corresponding to 0? So you have an eigenvalue 0. Let A be the 3X3 matrix. I was thinking of doing something like Ax=λx and substitute 0 for λ...

ahh ok so the matrix representation is what I said above and then you just check the properties of the idempotent apply

I honestly can not see the answer. Could you give me an example if you do not mind? It does not have to be this specific problem. maybe I am looking at the problem from a different angle if it is meant to be that obvious. is it 0.5 0 -0.5 0 1 0 -0.5 0 0.5

so if I multiply them I get ax+by+cz 0.5(x-z) dx+ey+fz = y gx+hy+iz 0.5(z-x) Is that what you meant? I am not sure where I am going with this.

ok so how would I square this matrix? if I write it in matrix form would it be 0.5x-0.5x y...

How do you show that a linear transformation is idempotent? T:R^3 to R^3 T (x y z)^T = (0.5 (x-z) , y, 0.5 (z-x)) I have no idea where to begin. I know a few facts about idempotent properties e.g such as their eigenvalues are...