# Homework 6: Ax=b

1. Solve the following linear system using Gaussian elimination. Show your work.

$\begin{pmatrix} 4 & 2 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 1 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \\ 0 \end{pmatrix}$

2. Solve the same system $\mod 3$. Show your work.
3. Given an efficient subroutine that takes integer $A,b$ as input and finds a rational $x$ such that $Ax=b$, give a simple, efficient algorithm to find a solution to $Ax=b \mod p$ for any prime $p$ that does not divide $\det(A)$.