Originally Posted by

**happystudent** true or false and why?

1) every square matrix can be written as the product of elementary matrices. Mr F says: False since the statement is not true when det(M) = 0.

2) The inverse of an elementary matrix is an elementary matrix. Mr F says:

True.

3) Every system with 3 equations in 4 unknowns has at least one solution. Mr F says:

False. It's not hard to come up with a counter-example to the statement.

4) A square matrix is defined to be stochastic if all its elements are nonnegative and the sum of the elements in any given column is 1.

Prove that the product of any two stochastic matrices is stochastic.

[snip]