unique, infinte solutins in matrices and determinants

for unique solution D not equals to 0 and D1,D2,D3 not simaltaneoysly zero
for infinite solution D=o and D1,D2,D3 equals to zero

wat abt dependenc n independence??

and is wat ram saidd it, aage kuch nahi??

wat abt eqtn in 2 var.??

a_{1}/a_{2}\neq b_{1}/b_{2}

UNIQUE SOLUTION

a_{1}/a_{2}= b_{1}/b_{2}\neq c_{1}/c_{2}

NO SOLUTION

a_{1}/a_{2}= b_{1}/b_{2}= c_{1}/c_{2}

INFINITE SOLUTIONS POSSIBLE

FOR UNIQUE SOLUTION

\Delta \neq 0

FOR NO SOLUTION

\Delta =0

PROVIDED THAT AT LEAST ONE OF \Delta _{X} \Delta _{Y} \Delta _{Z} IS NOT ZERO

FOR INFINITE SOLUTION \Delta _{Z} \Delta _{Y} \Delta _{Z} ALL ARE ZERO