Question

Math 22A Preparation I for Midterm 02 March 02, 2012 Problem 10 (10 points total) Suppose I tell you the nxn matrix A is NONSINGULAR. List as many conditions that are equivalent to A being nonsingular that you can, but no fewer than sir. (Keep adding to your list as the quarter goes on!)

Answer 1

Suppose n times n matrix A is NONSINGULAR then the following are equivalent 1 A is non singular 2 det A notequalto 0 3 Rows of A are linearly independent 4 Coloumns of A or linearly independent 5 Rank of A is n 6 Nullity of A is 0 7 For all n times 1 vector b Ax = b has only one solution in R^n