An Application of Linear Algebra |

Kevin McGoldrick - Math 345, Fall 2009 |

Least Squares Estimation The Key Result |

Theorem 3: Given that χ is the least squares solution to the system Ax = b, then χ is also a solution to the system A χ = (A
Proof: Suppose χ is a least squares solution to the system Ax = b. Then, multiplying both sides by A
With Theorem 3, we now have an efficient method of computing the least squares solution to an inconsistent system. The inconsistency guarantees that the columns of A are linearly independent. Thus, we need only compute the product (A |

The line above represents the least squares solution for the given points. |