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14.6

14.6. Solving Systems of 3 or More Variables. Why a Matrix?. In previous math classes you solved systems of two linear equations using the following method: Graphing Substitution Elimination.

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14.6

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  1. 14.6 Solving Systems of 3 or More Variables

  2. Why a Matrix? • In previous math classes you solved systems of two linear equations using the following method: • Graphing • Substitution • Elimination • These solutions were 2-dimensional (x, y). Matrices can also be used to solve systems of equations. They are especially useful in systems that involve 3 or more variables.

  3. We Live in a 3 Dimensional World, … Right? • Add the following points to the graph • (3, 4, 0) and (3, 4, -2) Look carefully at the example of graphing the 3 dimensional point (3,2,4). Where x=3, y=2, and z=4

  4. Solve by hand

  5. Using a Matrix to solve • First: Split the system into 3 matrices: • Matrix A holds the coefficients • Matrix X holds the variables • This matrix is called the vector matrix. • Matrix B hold the integer values to the right of the = sign. Ex 2:

  6. Sove for • To solve for “X”, we need to isolate matrix X by simplifying matrix A to “1” in matrix form. • We do this by multiplying Matrix A by it inverse matrix • So…to solve a system of equations using matrices we use: Now Solve example 2 again, this time using a matrix and your calculator.

  7. Now you try… Aren’t you glad you aren’t doing this by hand? 

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