First slide

System of linear equations

Question

The system of equation _{$4 x - 5 y - 2 z = 2$} ,_{$5 x - 4 y + 2 z = - 2$} ,_{$2 x + 2 y + 8 z = - 1$} is

Easy

A

Inconsistent
B

Consistent and determinate
C

Consistent but dependent
D

Either (a) or (c)

Solution

$t h e s y s t e m i s A X = B, w h e r e$
$A = [\begin{matrix} 4 & - 5 & - 2 \\ - 5 & - 4 & 2 \\ 2 & 2 & 8 \end{matrix}] X = [\begin{matrix} x \\ y \\ z \end{matrix}] B = [\begin{matrix} 2 \\ - 2 \\ - 1 \end{matrix}]$
$| A | = |\begin{matrix} 4 & - 5 & - 2 \\ 5 & - 4 & 2 \\ 2 & 2 & 8 \end{matrix}| = 0$
$∴ A^{- 1} d o e s n o t e x i s t$
$t h u s | A | = 0 . T h e r e f o r e t h e s y s t e m h a s n o s o l u t i o n .$

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