SOLUTION: Please help. Thanks. Ax = b is a linear system. If Ax = b cannot be solved by using cramers rule then A is not a square matrix. Is this true or false?

Algebra ->  Matrices-and-determiminant -> SOLUTION: Please help. Thanks. Ax = b is a linear system. If Ax = b cannot be solved by using cramers rule then A is not a square matrix. Is this true or false?       Log On


   

Question 582463: Please help. Thanks.
Ax = b is a linear system. If Ax = b cannot be solved by using cramers rule then A is not a square matrix. Is this true or false?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
False. If the determinant of a square matrix is zero, then you cannot use cramers rule because cramers rule has you dividing by the determinant (and you cannot divide by zero).

So basically, the fact that you cannot use cramers rule doesn't automatically mean that A is not a square matrix. The matrix A could be square, but it could also have a determinant of zero (which means that you can't use cramers rule)