1. Let, solve Ax = b for x using three different methods
(a) Find a LU decomposition of A and use substitution and back substitution to find x.
(b) Use Gaussian elimination on the augmented matrix.
(c) Use Gauss-Jordan elimination to find the inverse of A first and then let x = A−1x.
2. Row reduce the following matrix A and then find its rank, nullity, pivot columns and a basis for range(A) and null(A). Note, you could row-reduce it to an upper-triangular matrix or a non-reduced row echelon form or a reduced row echelon form. Row-reducing to an upper triangular matrix involves the least amount of row operations but reducing to a reduced row echelon form makes it easier to find the rank, nullity etc.
Ñ 1 2 1 3é
A = −3 2 1 0 .
3 2 1 1
