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Coordinates,Distance and Midpoint

Linear Inequalities

The Graphical Method

Substitution & Elimination

Solving Systems Using Matrices

Problem Solving

Systems of Inequalities

Systems with 3 Equations in 3 Unknowns

Review&Test

UNIT 2  : SYSTEMS OF EQUATIONS

LESSON 5 :  SOLVING SYSTEMS USING MATRICES

 

 

Definition:  A matrix is a rectangular array of numbers consisting of

rows and columns as below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note:  The Matrix Method may be used in place of either elimination or substitution.

 

          

 

Rectangular Callout: Strategies for the Matrix Method. § Write the system in matrix form using the coefficients and constant termsonly. § Find the LCM for the coefficients of either x or y. This will be the common coefficient. § Multiply both rows by appropriate numbers to obtain this common coefficient. § Add the 2 rows if the coefficients have different signs. § Subtract the 2 rows if the coefficients have the same sign. § Replace the second row by the result of the row operations above. § Return to Equation Form – there should be a zero in one of the first two positions of the second row. § Solve for the remaining variable. § Substitute the value of the solved variable in one of the original equations. § Solve for the second variable.

 


NOTE:  See lesson 8, Solving Systems with 3 Equations in 3 Unknowns for a more complete discussion

Of Solving Systems of Equations with Matrices.

 

 

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