A is a 3x2 matrix with two pivot positions.
(a) does the equation Ax=0 have a nontrivial solution
Since the two pivot positions will create 0 in the entire column in which they are present and 1 in its own position in reduced row echelon form and the rightmost column is all 0 therefore Ax=0 has no nontrivial solution
(b) does the equation Ax=b have atleast one solution for every possible b?
In the reduced row form b should have a [* * 0] form then only a unique non trivial solution exists
Is this correct and does it sound mathematical?