system of linear equations

Consider a system of linear equations Ax = b, where $$A = \left[ {\matrix{ 1 \hfill & { - \sqrt 2 } \hfill & 3 \hfill \cr { - 1} \hfill & {\sqrt 2 } \hfill & { - 3} \hfill \cr } }...

Consider the following system of linear equations. $$ x_1+2 x_2=b_1 ; 2 x_1+4 x_2=b_2 ; 3 x_1+7 x_2=b_3 ; 3 x_1+9 x_2=b_4 $$ Which one of the following conditions ensures that a so...

Consider system of linear equations : $$$x-2y+3z=-1$$$ $$$x-3y+4z=1$$$ and $$$-2x+4y-6z=k,$$$ The value of $$'k'$$ for which the system has infinitely many solutions is _______.