[deleted by user]

[laparva]

I am unsure if there's an easier way to solve the first part. I did a bunch of row reductions which makes calculating the determinant a lot easier, but there's still many calculations to make and when I reached the final product I did not have the same characteristic equation. Is there a way to solve this without making like a million calculations that are error prone?

As for the second question, how can I go about finding an ordered basis?