Question 751018
<pre>
A=[1 -1  0] 
  [1  0 -1]  
  [6 -2 -3] 

B=[-2 -3 1]
  [-3 -3 1]
  [-2 -4 1]
</pre>
Solve for X: 3X+4B=A
<pre>
{{{3}}}{{{""*""}}}{{{X}}}{{{""+""}}}{{{4}}}{{{""*""}}}{{{B}}}{{{""=""}}}{{{A}}}

     {{{3}}}{{{""*""}}}{{{X}}}{{{""=""}}}{{{A}}}{{{""-""}}}{{{4}}}{{{""*""}}}{{{B}}}

Consider the minus sign before the 4 as a plus sign times (-4).
That's because we'd rather add matrices than subtract them:

     {{{3}}}{{{""*""}}}{{{X}}}{{{""=""}}}{{{A}}}{{{""+""}}}{{{(-4)}}}{{{""*""}}}{{{B}}}

Substitute the matrices in the equation for the letters:

{{{3}}}{{{""*""}}} {{{X}}}{{{""=""}}}{{{(matrix(3,3,
  1, -1,  0, 
  1,  0, -1,  
  6, -2, -3))}}}{{{""+""}}}{{{(-4)}}}{{{""*""}}}{{{(matrix(3,3,
  -2, -3, 1,
  -3, -3, 1,
  -2, -4, 1))}}}

Distribute the (-4) by multiplying it by all 9 elements of the 
matrix on the far right:

{{{3}}}{{{""*""}}} {{{X}}}{{{""=""}}}{{{(matrix(3,3,
  1, -1,  0, 
  1,  0, -1,  
  6, -2, -3))}}}{{{""+""}}}{{{(matrix(3,3,
  8, 12, -4,
  12, 12, -4,
  8, 16, -4))}}}

We add the corresponding elements of the matrices on the right:

{{{3}}}{{{""*""}}} {{{X}}}{{{""=""}}}{{{(matrix(3,3,
  9, 11, -4, 
  13, 12, -5,  
  14, 14, -7))}}}

Finally we multiply both sides by {{{1/3}}}

{{{(1/3)}}}{{{""*""}}}{{{3}}}{{{""*""}}}{{{X}}}{{{""=""}}}{{{(1/3)}}}{{{""*""}}}{{{(matrix(3,3,
  9, 11, -4, 
  13, 12, -5,  
  14, 14, -7))}}}


Distribute the {{{1/3}}} by multiplying it by all 9 elements of the 
matrix on the right:

{{{X}}}{{{""=""}}}{{{(matrix(3,3,
  3, 11/3, -4/3, 
  13/3, 4, -5/3,  
  14/3, 14/3, -7/3))}}}   

Edwin</pre>