Question 1124978
{{{ (matrix(4,4, 1,1,1,1,  2,-1,1,-2, 3,1,-2,-1, 4,-1,3,-1)) * (matrix(4,1,  a,b,c,d)) = (matrix(4,1, 7,-13,5,-10) ) }}}<br>

We have  <b>Ax = b</b> and the solution we want is  <b>BAx=Bb</b>  where B is {{{A^-1}}}<br>

Using your favorite matrix inverter website and/or computing by hand:
B = {{{ (1/19)*(matrix(4,4, -5,-8,4,7, 25,21,-1,-16,  11,10,-5,-4,  -12,-23,2,13)) }}} <br>

So {{{ (matrix(4,1, a,b,c,d)) = (1/19)*(matrix(4,4, -5,-8,4,7, 25,21,-1,-16,  11,10,-5,-4,  -12,-23,2,13))* (matrix(4,1, 7,-13,5,-10)) }}} ==>  {{{ highlight( (matrix(4,1, a,b,c,d)) =  (matrix(4,1, 1,3,-2,5)) ) }}} <br>


Check: 
  1+3+(-2)+5 = 7 (ok)
  2(1)-3+(-2)-2(5) = -13 (ok)
  3(1)+3-2(-2)-5 = 5  (ok)       
  4(1)-3+3(-2)-5 = -10 (ok)