The biggest challenge for me in attempting this problem is using the Linear algebra.
If I'm correct, I must:
1) Find eigenvalues.
2) Find eigenvectors.
3) Compute e^(At)
4) Multiply e^(At) by y_0 = y(0)
So, assuming what I said is correct, it seems like I know what I am doing but it's in setting up each step and then taking the result and moving to the next step that loses me so I would really appreciate if someone could show me how to set up each step and the answer each step gives to feed into the next step. I don't need mechanical computations (software outputs should most likely be fine).
Any help would be GREATLY appreciated!
Thanks in advance!
Sorry for the late reply, I was having difficulty computing things. I'm attaching my work so far. Hopefully, it's correct.
Also, I know this is minor in comparison to my other problems but, instead of u_1, u_2, u_3 and w_1, w_2, w_3, should I have reused the v_i notation (strictly speaking) or was I technically correct to use different variables?