In Exercises 29-32, (a) does the equation Ax = 0 have a nontriv- ial solution and (b) does the equation Ax = b have at least one solution for every possible b? 29. A is a 3 x 3 matrix with three pivot positions.

Introduction:

Pivots in a matrix;

1. Any row that does not contain only zeros its first non zero number is a 1 also is called the leading 1. These are also called pivots.
2. For two successive rows with leading 1's, the 1 in the lower row is to the right of the 1 in the upper row. 

Given:  A is a $3\times 3$ matrix with three pivot positions.

To find:

Justify the solutions for the system.