How to solve for x?

Question

|X   12   13|

|0   X-2  23| =0

|0    0   X-4|  

Answer 1

This is an upper triangular matrix so the determinant is the product of the diagonal elements which is 

 

X*(X-2)*(X-4) 

 

So X = 0, X = 2 and X=4 are the solutions that will make the determinant 0