Question 923156
Let
{{{x=(matrix(2,2,a,b,c,d))}}}
Then,
{{{(matrix(2,2,5,4,1,1))*(matrix(2,2,a,b,c,d))=(matrix(2,2,1,-2,1,3))}}}
Looking at each element,
1.{{{5a+4c=1}}}
2.{{{5b+4d=-2}}}
3.{{{a+c=1}}}
4.{{{b+d=3}}}
From eq. 3,
{{{a=1-c}}}
From eq. 4,
{{{b=3-d}}}
Substitute in eq. 1 and 2,
{{{5(1-c)+4c=1}}}
{{{5-5c+4c=1}}}
{{{5-c=1}}}
{{{c=4}}}
Then,
{{{a=1-4=-3}}}
.
.
{{{5(3-d)+4d=-2}}}
{{{15-5d+4d=-2}}}
{{{15-d=-2}}}
{{{-d=-17}}}
{{{d=17}}}
Then,
{{{b=3-17=-14}}}
So then,
{{{x=(matrix(2,2,-3,-14,4,17))}}}