Given: \[{{L}_{1}}~=\text{ }\left( b\text{ }+\text{ }c \right)x\text{ }+\text{ }ay\text{ }+\text{ }1\text{ }=\text{ }0\] \[{{L}_{2}}~=\text{ }\left( c\text{ }+\text{ }a \right)x\text{ }+\text{...

Given: \[{{p}_{1}}x\text{ }+\text{ }{{q}_{1}}y\text{ }=\text{ }1\] \[{{p}_{2}}x\text{ }+\text{ }{{q}_{2}}y\text{ }=\text{ }1\] and , \[{{p}_{3}}x\text{ }+\text{ }{{q}_{3}}y\text{ }=\text{ }1\] The...

Given: \[{{m}_{1}}x\text{ }\text{ }y\text{ }+\text{ }{{c}_{1}}~=\text{ }0\text{ }\ldots \text{ }\left( 1 \right)\] \[{{m}_{2}}x\text{ }\text{ }y\text{ }+\text{ }{{c}_{2}}~=\text{ }0\text{ }\ldots...

Given: \[2x~-~5y\text{ }+\text{ }3\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 1 \right)\] \[5x~-~9y\text{ }+~\lambda ~=\text{ }0\text{ }\ldots \text{ }\left( 2 \right)\] And , \[x~-~2y\text{...

\[\left( \mathbf{i} \right)~15x\text{ }\text{ }18y\text{ }+\text{ }1\text{ }=\text{ }0,\text{ }12x\text{ }+\text{ }10y\text{ }\text{ }3\text{ }=\text{ }0\] and \[6x\text{ }+\text{ }66y\text{ }\text{...