# 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.

© BrainMass Inc. brainmass.com October 9, 2019, 7:24 pm ad1c9bdddfhttps://brainmass.com/math/matrices/matrices-pivot-positions-solutions-ax-ax-b-117061

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

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

#### Solution Summary

Matrices, pivot positions and solutions for Ax+0 and Ax=b are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.