Quiz3Matrices: Problem 9

(1 pt) Consider the following two systems.

(a)

$\begin{array}{ccc} 6 x- y &=& -2 \\ - x - 7 y &=& -3 \end{array}$

(b)

$\begin{array}{ccc} 6 x- y &=& 1 \\ - x - 7 y &=& -2 \end{array}$

(i) Find the inverse of the (common) coefficient matrix of the two systems.

$A^{-1} =$	$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$			$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating $A^{-1} b$ where represents the right hand side (i.e. $b = \left[ \begin{array}{c} -2 \\ -3 \end{array} \right]$ for system (a) and $b = \left[ \begin{array}{c} 1 \\ -2 \end{array} \right]$ for system (b)).