Solving a system of equations by using matrices is merely an organized manner of using the elimination method.
Example 1: Solve this system of equations by using matrices.
The goal is to arrive at a matrix of the following form.
To do this, you use row multiplications, row additions, or row switching, as shown in the following.
Put the equation in matrix form.
Eliminate the
x-coefficient.
Eliminate the
y-coefficient.
Reinserting the variables, this system is now
Equation (9) can now be solved for
z. That result is substituted into equation (8), which is then solved for
y. The values for
z and
y are then substituted into equation (7), which is then solved for
x.
The check is left to you. The solution is
x = 2,
y = 1,
z = 3.
Example 2: Solve the following system of equations, using matrices.
Put the equations in matrix form.
Eliminate the
x-coefficient.
Eliminate the
y-coefficient.
Reinserting the variables, the system is now
Equation (9) can be solved for
z.
Substitute
z = –5/6 into equation (8) and solve for
y.
Substitute
y = ⅔ and
z = –5/6 into equation (7) and solve for
x.
The check of the solution is left to you. The solution is
x = ½,
y = ⅔,
z = –5/6.
Linear Sentences in One Variable
Linear Equations In Three Variables
