Description
1. Let A =
Å
2 3
1 4ã
, b =
Å
1
3
ã
, 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.
A =
Ñ
1 2 1 3
−3 2 1 0
3 2 1 1é
.
