Question 173474
<pre><font size = 4 color = "indigo"><b>

{{{(matrix(2,2,-3,-14,2,9))X=(matrix(2,2,8,-4,0,-4))}}}

First find the inverse of {{{(matrix(2,2,-3,-14,2,9))}}} by

1. find the determinant 

{{{matrix(1,7,   abs(matrix(2,2,-3,-14,2,9)), "=", (-3)(9)-(-14)(2), "=", -27+28,"=",1)}}}

2. Swap the elements is the upper left to lower right diagonal.
   Change the signs in the other diagonal.

{{{(matrix(2,2,-9,14,2,3))}}}


3. Divide the matrix through by the determinant

{{{matrix(1,5,(matrix(2,2,-9,14,2,3)), "÷", 1, "=", (matrix(2,2,-9,14,2,3)) )}}} 

That is the inverse matrix. So left-multiply both sides
of the original equation by this inverse:

{{{(matrix(2,2,-3,-14,2,9))X=(matrix(2,2,8,-4,0,-4))}}}

{{{(matrix(2,2,-9,14,2,3))(matrix(2,2,-3,-14,2,9))X=(matrix(2,2,-9,14,2,3))(matrix(2,2,8,-4,0,-4))}}}


{{{(matrix(2,2,1,0,0,1))X=(matrix(2,2,-72,-20,16,-20))}}}

{{{X=(matrix(2,2,-72,-20,16,-20))}}}

Edwin</pre>