An infeasible linear system
The system of 
equations in 
unknowns is
which can be written as 
, where 
is the 
matrix
![\[ A = \left( \begin{array}{cc} 3 & 4.5 \\ 2 & 1.2 \\ -0.1 & 8.2 \\ \end{array} \right), \]](https://pressbooks.pub/app/uploads/quicklatex/quicklatex.com-5e26a12e34c8c1f0190713a69636167c_l3.png "Rendered by QuickLaTeX.com")
and 
is the -vector
![\[ y = \left( \begin{array}{c} 1 \\ -3.2 \\ 1.5 \\ \end{array} \right). \]](https://pressbooks.pub/app/uploads/quicklatex/quicklatex.com-1bf4c95dbfd67921929ceb1bc5018f9c_l3.png "Rendered by QuickLaTeX.com")
The set of solutions turns out to be empty. Indeed, if we use the first two equations, and solve for 
, we get 
, but then the last equation is not satisfied, since
![\[-0.1 x_1 + 8.2 x_2 = 17.4741 \neq 1.5. \]](https://pressbooks.pub/app/uploads/quicklatex/quicklatex.com-688ac6524a1d413130ba27357d39618f_l3.png "Rendered by QuickLaTeX.com")
