Solved: A system of linear equations with fewer equations

Solution

Step 1 of 3

A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Suppose that such a system happens to be consistent.

Let A represent the augmented matrix for the system.We have some condition to determine the system is consistent or not.

1. The number of pivots of A is less than equal to the number of rows of A
2. The number of pivots of A is equal to the number of equations in the system
3. The number of pivots of A is less than but not equal to the number of unknowns in the system.
4. The number of pivots of A  = (the number of columns of A) - 1.