Exercise Prove that for any square matrix ` A`,
there are unique symmetric matrix

Exercise Prove that if ` A` is invertible,
then

Exercise By making use of the computation in this exercise, solve the following systems.

2x_{1} |
+ 7x_{2} |
= | 2 |

3x_{1} |
+ 9x_{2} |
= | -1 |

x_{1} |
+ 2x_{2} |
+ 4x_{3} |
= | 1 |

- x_{2} |
- x_{3} |
= | 0 | |

2x_{1} |
+ 3x_{2} |
+ 8x_{3} |
= | -1 |

2x_{1} |
+ x_{2} |
+ x_{4} |
= | 1 | |

x_{2} |
+ x_{3} |
- x_{4} |
= | 0 | |

2x_{1} |
- x_{2} |
- 2x_{3} |
+ 2x_{4} |
= | 1 |

x_{1} |
- x_{3} |
+ x_{4} |
= | 0 |