Answer to Question #173508 in Linear Algebra for ANJU JAYACHANDRAN

Question

9(b) Consider the system of equations (5)

11 2x1 + x2 + 4x3 =

3x1 + x2 + 5x3 =14

A feasible solution is x1 = ,2 x2 = ,3 x3 = .1 Reduce this feasible solution to a basic

feasible solution.

Answer 1

$2x_1+x_2=11-4x_3$

$3x_1+x_2=14-5x_3$

$\Delta=\begin{vmatrix} 2 & 1 \\ 3 & 1 \end{vmatrix}=-1$

$\Delta_1=\begin{vmatrix} 11-4x_3 & 1 \\ 14-5x_3 & 1 \end{vmatrix}=x_3-3$

$\Delta_2=\begin{vmatrix} 2 & 11-4x_3 \\ 3 & 14-5x_3 \end{vmatrix}=2x_3-5$

$x_1=\Delta_1/\Delta=3-x_3$

$x_2=\Delta_2/\Delta=5-2x_3$