Write the system in equation form?

[mathrocks]

Hi, I'm given a matrix and I need to write it in equation form so that I will have three equations, using x(t), y(t), and z(t)

The matrix is a 3x3
[3 -2 0]
x'= [-1 3 -2] *x
[0 -1 3]

I know how to rewrite it using only x(t) but I'm not sure how to do it using y(t) and z(t).

thanks!

[HallsofIvy]

Your problem may be that you are using " x(t)" in two different ways- as a vector function and as a component of the vector. Your
[3 -2 1]
[-1 3 2] x
[0 -1 3]

is the same as

[3 -2 1][x(t)]
[-1 3 2][y(t)]
[0 -1 3][z(t)]

Do the matrix multiplication: that's
[3x(t)- 2y(t)+ z(t)]
[-x(t)+ 3y(t)+2z(t)]
[0x(t)- y(t)+3z(t)]

so your system of differential equations is x'(t)= 3x(t)- 2y(t)+ z(t),
y'(t)= -x(t)+ 3y(t)+ 2z(t), and z'(t) -y(t)+ 3z(t).