A
matrix (plural,
matrices) is a rectangular array of numbers or variables. A matrix can be used to represent a system of equations in standard form by writing only the coefficients of the variables and the constants in the equations.
Example 1: Represent this system as a matrix.
In the matrix above, the dashed line separates the coefficients of the variables from the constants in each equation.
Through the use of row multiplication and row additions, the goal is to transform the preceding matrix into the following form.
The matrix method is the same as the elimination method but more organized.
Example 2: Solve this system by using matrices.
This matrix now represents the system
Therefore,
y = 1
Now, substitute 1 for
y in the other equation and solve for
x.
Check the solution.
The solution is
x = 3,
y = 1.
Matrices will be more useful when solving a system of three equations in three unknowns.
Linear Sentences in One Variable
Linear Sentences In Two Variables
