"Hi teacher
1.can you show how to get this L? I dont know why but i cant solve it.
2. We find L in order to find x (in UX=y) right?
3. What is trivial solution
Thank you"

1. You copied down L incorrectly - probably because I originally wrote it wrong in the lecture then scribbled over the correct one. Check the lecture notes again and you will see that the 2nd row, 3rd column should be 0. The file below details the calculation of L.

2. We find L so that we can write Ly=b. We know L and we know b so we can simply read off the values of y since L is triangular. After this we write Ux=y, from which we now know both U and y so we can read off the values of x.

3. Trivial solution just means that the answer to the linear system is the zero vector.