Consider the matrix

1 2 1

1 4 3

2 2 1

Note: a = 1

1. Each step of the Gaussian elimination process applied to A is associated with left multiplication by a particular lower-triangular 3 3 matrix. Review the Gaussian elimination process and identify the associated lower-triangular matrices.
2. Using your answer to part 1, express A as a product A = LU where L is lower triangular and U is upper triangular.