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 preceding matrix, 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.
Multiply 2 times row 1 and –5 times row 2; then add: 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 are a more time‐consuming method of solving systems of linear equations than either the elimination or substitution methods. They only become a time‐saving method when solving multiple equations in multiple variables that are repeatedly equated to different sets of constants. Don't worry; you won't have to do those this year. Still, you should know that they are an alternative method of solving linear equation systems. Download Article Download Article A matrix is a very useful way of representing numbers in a block format,[1] which you can then use to solve a system of linear equations. If you only have two variables, you will probably use a different method. See Solve a System of Two Linear Equations and Solve Systems of Equations for examples of these other methods. But when you have three or more variables, a matrix is ideal. By using repeated combinations of multiplication and addition, you can systematically reach a solution.
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ReferencesAbout This ArticleArticle SummaryX By properly setting up a matrix, you can use them to solve a system of linear equations. Start by writing out your equations and then transfer the numbers from them into a matrix by copying the coefficients and results into a single row. Stack the rows one on top of each other to form a block-looking format. Add a large square bracket around your full matrix and use the abbreviation “R” for the rows and “C” for the columns. This allows you to refer to a specific position in the matrix with a combination of R and C, such as R4C1. To solve the matrix, you can use different operations. For instance, you could use row-addition or row-subtraction, which allows you to add or subtract any two rows of the matrix. To learn about other ways to create a solution matrix, keep reading! Did this summary help you? Thanks to all authors for creating a page that has been read 118,063 times. Did this article help you? |