Problems:
In problems 1-4 (a) does the equation Ax=0 have a nontrivial solution and (b) does the equation the Ax=b have at least one solution for every possible b?
1) A is a 3x3 matrix with three pivot positions.
2) A is a 3x3 matrix with two pivot positions.
3) A is a 3x2 matrix with two pivot positions.
4) A is a 2x4 matrix with two pivot positions.
2) Given
A= 
find one nontrivial solution of Ax=0 by inspection. (Hint: think of the equation Ax=0 written as a vector equation.
NOTE: the numbers in the matrix are row#1 = -2 and -6, row#2 = 7 and 21, row #3 = -3 and -9.