Did you mean to put a quantity of chemical X there? I don't see a number.

Same issue here.of a chemical X is dissolved into tank A, and tank B has kg

Why are there t's in these equations? What is your justification for your answer of this part of the problem?of the same chemical X dissolved into it.

i). Write down the system of differential equations satisfied by x(t) and y(t), the quantity of the chemical X in tanks A and B respectively.

x(t)=x0-t(y0/40-x0/40)

y(t)=y0-(y0/40+x0/40)

dx/dt=t(-y0/40+x0/40)

dy/dt=t(y0/40-x0/40)

I agree with your matrix form. That is, the DE can be written asii). Find the eigenvalues and the eigenvectors of the resulting matrix form.

The matrix is

(-1/40 1/40)

(1/40 -1/40)

If you let

then the solution to this differential equation is

What you must do is make sense of the exponential How do you do matrix exponentiation? This is how you can finish the problem.

The eigenvalues are 0 and -2

so the eigenvector are

(-1)

(1 )

and

(1)

(1)

iii). Show that the amount of the chemical X in either tank approaches as t approaches infinity.

i dont have any idea to do this part, can anyone help me? and tell me what i did wrong in the first and second part pls