Question

You have a matrix A for
Ax=0
Linear independence states that in order the columns for matrix A to be linear independent that Ax=0 must only have the trivial solution. Is this true?

Answer 1

We can row reduce the augment matrix to see if there is a zero row or in other words a free variable. But what's confusing me is that if there is if x was a zero vector right?

Answer 2

Another thing is that my book showed that the augmented form proved that the columsn were lin independent BUT
the last row was

0 0 19 0
How can 19=0???
there is no solution!!!

Answer 3

your first statement is true