Let T Rn rightarrow Rm be a liner transformation A its matr

Let T : R^n rightarrow R^m be a liner transformation, A its matrix. Complete fllowing to-one if and only if A has piVot, columns. And show your proof for this statement.

Solution

The matrix A must have n   pivot columns.

Explaination :

T is one to one iff the only solution to Ax = 0 is x = 0. This means \"no free variables\" in solution, which happens when there is a pivot in every column. Since the number of columns is n, then there are n pivot columns.