Matrix Reloaded [Log 04]: How to find out whether the solution to a system of linear equations is unique, infinite, or if the system is inconsistent?
How to find out whether the solution to a system of linear equations is unique, infinite, or if the system is inconsistent? Here’s a little recap of the basics: The solution to a system of linear equations is unique if it has one definite value for each variable. The solution is infinite if there are infinite possibilities for the values of one or more variables. The system is inconsistent if there is no possible solution. Let’s start the topic with an example: This is a Reduced Row Echelon Form of an augmented matrix: [ 1 0 − 9 1 0 1 1 3 0 0 0 0 ] \begin {bmatrix} 1 & 0 & -5 & 1\\ 0 & 1 & 1 & 4\\ 0 & 0 & 0 & 0 \end {bmatrix} Turn this into its linear equation format: x - 9z = 1 y + z = 3 0 = 0 0 equals 0 is technically true, so all the equations are valid, and thus the system is consistent. Now, let’s talk about basic variables and free variables: Basic variables are variables corresponding to pivot columns in the matri...
