Linear systems of equations, sets and lists, and the solve command

Variables, equations and other objects in Maple can be grouped together and given a name for the group of objects. If this grouping of objects has a special order from left to right then the group is called a “list”. If the grouping has no particular order then it is called a “set:” Lists are enclosed in square brackets […] and sets are enclosed in curly brackets {…}. The use of sets is particularly important when you want to solve a number of equations for a number of unknowns. The use of lists is important when you want to use the plot command to plot several expressions on the same graph. Each of these sets and lists has other uses as well. Often a solution with multiple parts is displayed as a set and you will need to select particular solution elements from the set. You can always identify a set because it is enclosed in curly brackets {…}.

The solutions to multiple algebraic equations in multiple unknowns can be found using the solve command by grouping the equations and unknowns together in sets. The solve command will return the symbolic solution to the equations just as it did for a single equation. A common form of multiple equations is systems of linear equations. Linear equations are ones where the unknowns all appear with an exponent of one. Of course linear algebra is a whole subject unto itself. For this lesson we consider small systems of linear equations; ones with only two or three or four unknowns.