+riangularize the operator T: C^3 --> C^3 given by T(x,y,z)= (x, yi, y+zi). Find the ordered basis B and the upper triangular matrix Mat(T, B ,B).

This is what I have so far, please let me know how it looks. Thanks!

Standard basis : (1,0,0)=(1,0,0) (0,1,0)=(0, i, 1) (0,0,1)=(0,0, i) What do you mean with these weird equalities?? The 2nd and 3rd. ones are obviously false...

Take simply the standard basis ... Apply i times the second row and add to the third. Now I have (1,0,0) (0, i, 0) (0,1, i) So the eigen values are {1,i}