# Matrices and Pivot Positions : Solutions for Ax+0 and Ax=b

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.

See attached file for full problem description.

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In problems 1-4 (a) does the equation Ax=0 have a nontrivial solution and (b) does the equation Ax=b ...

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