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Solve Systems using Inverse Matrices

Solve Systems using Inverse Matrices

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Author: Zach Cresswell
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Tutorial

Solve Systems using matrices

Source: Khan Academy - Sal Khan

Tips

More TIps

This same method works for 3 equations and 3 unknowns! Or More!

In other words, in the system:

3x+2y-z=1

1x+4y-5z=15

-6x+4y-7z = -4

 

 

We could set up the matrix equation:

open square brackets table row 3 2 cell negative 1 end cell row 1 4 cell negative 5 end cell row cell negative 6 end cell 4 cell negative 7 end cell end table close square brackets open square brackets table row x row y row z end table close square brackets equals open square brackets table row 1 row 15 row cell negative 4 end cell end table close square brackets
space space space space space space space space space space space A space space space space space space space space space space space space space X space space space equals space space space space space space space space B

To solve: 

A-1A X = A-1 B  (Order matters! You cannot multiply B(A-1)

    X = A-1