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Dr. Shildneck Fall, 2015 SOLVING SYSTEMS OF EQUATIONS USING MATRICES

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MULTIPLY THE FOLLOWING

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NOW, TAKE THAT ANSWER AND SET EQUAL TO

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SO, NOW WE HAVE…

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WHICH THROUGH EQUIVALENT MATRICES GIVES US THE SYSTEM… NOW SOLVE THE SYSTEM…

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YOU SHOULD HAVE GOTTEN THE ANSWER… (-2, 2)

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NEXT, LET’S USE INVERSE MATRICES TO SOLVE THE MATRIX EQUATION…

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FIRST, FIND THE INVERSE OF THE MULTIPLIER… Determinant =-2 – 15 =-17

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NEXT, MULTIPLY BOTH SIDES BY THE INVERSE…

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WHAT DO YOU NOTICE? So, what do you notice about our answers to the system and the matrix equation? What do you think Matrix X was?

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GIVEN THAT THIS SYSTEM HAD THE SAME ANSWER AS THIS MATRIX EQUATION… WHAT CAN YOU CONCLUDE ABOUT HOW THE SYSTEM AND MATRIX EQUATION RELATE?

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USE YOUR CONCLUSION TO WRITE THE FOLLOWIG SYSTEM AS A MATRIX EQUATION

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DID YOU GET… COEFFICIENTS Matrix VARIABLES Matrix ARGUMENTS Matrix

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TRY WRITING THIS SYSTEM AS A MATRIX EQUATION

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SYSTEMS AND MATRICES The fact that we can write and NxN system as a Matrix Equation allows us to use Inverse Matrices to solve the Matrix Equation rather than multi- step algebraic manipulations. Furthermore, for systems bigger than 2x2, this process allows us to quickly solve the system in one step, rather than a page full of steps!

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SYSTEMS AND MATRICES The process for solving any system of equations using matrices is as follows: 1.Write the system as a matrix equation AX=B, where A = the coefficient matrix, X = the variable matrix, and B = the argument matrix 2.Find the inverse of A and multiply. 3.The solution to the system is given by X = A -1 B

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EXAMPLE 1 – USING A CALCULATOR Step 1: Write the Matrix Equation. Step 2: Enter Matrix A and Matrix B in the calculator. Step 3: Solve by multiplying A -1 B. Step 4: Write the solution as a set of coordinates.

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EXAMPLE 2 – USING A CALCULATOR

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ASSIGNMENT ASSIGNMENT #8 – Solving Systems of Equations with Matrices

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