Abstract
This paper strives to prove different invertible matrices theorems.
The following are some of the theorems that the paper will justify
- A is an invertible matrix
- A is row equivalent to the n × n identity matrix
- A has n pivot positions
- The equation Ax=0 has only the trivial solution
- The equation Ax=b has at least one solution for each b in RN.
- The columns of A spans RN
- The linear transformation X→Ax maps RN onto RN.
- There is an n × n matrix ...