# Find the inverse of 3x3 matrix and show steps involved?

The logic behind finding an inverse is something I can not currently grasp, can someone help me figure out how to find the inverse of a matrix:

[5, 30, 242.5;

30, 242.5, 2205;

242.5, 2205, 21308.125]

Thanks!

Relevance
• cidyah
Lv 7
8 years ago

5 | 30 | 242.5 | 1 | 0 | 0 |

30 | 242.5 | 2205 | 0 | 1 | 0 |

242.5 | 2205 | 21308.125 | 0 | 0 | 1 |

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1 | 6 | 48.5 | 0.2 | 0 | 0 |

0 | 62.5 | 750 | -6 | 1 | 0 |

0 | 750 | 9546.875 | -48.5 | 0 | 1 |

------------------

1 | 6 | 48.5 | 0.2 | 0 | 0 |

0 | 1 | 12 | -0.096 | 0.016 | 0 |

0 | 0 | 546.875 | 23.5 | -12 | 1 |

------------------

1 | 6 | 48.5 | 0.2 | 0 | 0 |

0 | 1 | 12 | -0.096 | 0.016 | 0 |

0 | 0 | 1 | 0.043 | -0.0219 | 0.0018 |

------------------

1 | 6 | 0 | -1.8841 | 1.0642 | -0.0887 |

0 | 1 | 0 | -0.6117 | 0.2793 | -0.0219 |

0 | 0 | 1 | 0.043 | -0.0219 | 0.0018 |

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1 | 0 | 0 | 1.7858 | -0.6117 | 0.043 |

0 | 1 | 0 | -0.6117 | 0.2793 | -0.0219 |

0 | 0 | 1 | 0.043 | -0.0219 | 0.0018 |

------------------

The inverse matrix appears on the right followed by the identity matrix.

It is also symmetric. We use the Gauss-Jordan elimination method on the matrix at the beginning.

• 4 years ago

set up a 3x6 matrix the place the left a million/2 is the unique 3x3 matrix and the ideal suited a million/2 is the 3x3 identity matrix. Then do row operations till the left a million/2 will become the identity matrix. as quickly as you do this, the 3x3 matrix on the ideal suited a million/2 could be the inverse.