A= [0 1

3 2 ]

1. What is the LU (lower-upper) decomposition for the matrix A given above . It means calculate L and U matrices so that LU = A
2. Prove that when L and U matrices calculated in a) give matrix A when multiplied . Prove that LU = A using these matrices.
3. Is there a problem in calculating the LU decomposition for matrix A? If not simply say NO. If yes explain why and explain whether it is possible to overcome this problem