$$ B=\left[ \begin{array} k1 & 0 & 2 & 1\\ -3 & 2 &-1 & 5\\ 2 & -1 & 1 & 4\\ 0 & 3 & 2 & 4\\ \end{array} \right] $$
I have to find all the solutions of the system $Bx =\left[ \begin{array} k7\\ -10\\ 7\\ 0\\ \end{array} \right]$
What is $Bx$ exactly? Is that just simply the matrix $B$ multiplied by $x$? Therefore:
$$ Bx=\left[ \begin{array} kx & 0 & 2x & x\\ -3x & 2x &-x & 5x\\ 2x & -x & x & 4x\\ 0 & 3x & 2x & 4x\\ \end{array} \right] $$
But how can I find all the solutions to this equation? I am clueless as to how to solve this, please help!
Hint: find the inverse of B and then multiply both sides of the equation Bx = c by such an inverse. This leads to
inv(B) B x = inv(B)c , x = inv(B)c .