<P> The equations of a linear system are independent if none of the equations can be derived algebraically from the others . When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set . For linear equations, logical independence is the same as linear independence . </P> <P> For example, the equations </P> <Dl> <Dd> 3 x + 2 y = 6 and 6 x + 4 y = 12 (\ displaystyle 3x + 2y = 6 \; \; \; \; (\ text (and)) \; \; \; \; 6x + 4y = 12) </Dd> </Dl> <Dd> 3 x + 2 y = 6 and 6 x + 4 y = 12 (\ displaystyle 3x + 2y = 6 \; \; \; \; (\ text (and)) \; \; \; \; 6x + 4y = 12) </Dd>

The matrix derived from a system of linear equations is called the matrix of the system