Final answer:
The LU-factorization of the matrix [1 -3] [0 1] is L = [1 0] [0 1] and U = [1 -3] [0 1].
Step-by-step explanation:
To find the LU-factorization of the given matrix, we need to decompose it into a lower triangular matrix (L) and an upper triangular matrix (U) such that A = LU. Additionally, the L matrix must have a unit diagonal. The LU-factorization of the matrix [1 -3] [0 1] is L = [1 0] [0 1] and U = [1 -3] [0 1].