Ten of these equivalent statements are given below:
• 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 span Rn.
• The linear transformation x? Axmaps Rn onto Rn.
• There is an n× n matrix C such that CA = I.
• There is an n× n matrix Dsuch that AD = I.
• The columns of A form a basis of Rn.
Justify that the ten statements are logically equivalent to the statement “The n × n matrix Ais invertible."
Note:
1. It does not have to be a-> b > c. However they all have to connect in some way.
2. This is the exact same assignment as the last one I paid for but never got original work. THIS MUST BE ORIGINAL WORK.