[Solved] MATH307 Group Homework10

Instructions: Due the beginning of the next class (no late homework is accepted). Read textbook pages 114-117 before working on the homework problems. Show all steps to get full credits.

1. Let, solve Ax = b for x using three different methods
   • Find a LU decomposition of A and use substitution and back substitution to find x.
   • Use Gaussian elimination on the augmented matrix.
   • Use Gauss-Jordan elimination to find the inverse of A first and then let x = A¹x.
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.

1 2 1 3

A = 3 2 1 0 .

3 2 1 1