If the system of linear equations x - 4y + 7z = g 3y - 5z = h -2x + 5y - 9z = k is consist…

Question

If the system of linear equations

x - 4y + 7z = g

3y - 5z = h

-2x + 5y - 9z = k

is consistent, then :

Accepted Answer

x - $4y + 7z = g$

$3y$ - $5z = h$

- $2x + 5y$$-$$9z = k$$D = \left| {\begin{pmatrix} 1 & { - 4} & 7  \
   0 & 3 & { - 5}  \
   { - 2} & 5 & { - 9}  \

\end{pmatrix} } ight|$$D = 1\left( { - 27 + 25} ight) - 2\left( {20 - 21} ight) (

\]D =  - 2 + 2 = 0$If system is consistent then${D_1} = {D_2} = {D_3} = 0$$\left| {\begin{pmatrix} 1 & { - 4} & g  \
   0 & 3 & h  \
   { - 2} & 5 & k  \

\end{pmatrix} } ight| = 0$$1\left( {3k - 5h} ight) - 2\left( { - 4h - 3g} ight) = 0$$3k - 5h + 8h + 6g = 0$$6g + 3h + 3k = 0$$2g + h + k = 0$

Solutions · 1