Given that , determine the values of ,
, , and .
To determine the values of and , the individual
elements in each matrix must be equated and then the resulting
simultaneous equations solved.
You are given that
Equating each of the four elements gives the following four equations:
Now solve these equations. Begin by solving the first two equations simultaneously. Adding the two equations together will eliminate the and give
Now substitute this value of into the second equation. This will enable you to find :
Now substitute the values of both and into the third equation. This will enable you to find :
Finally substitute the values of and into the fourth equation. This will enable you to find :
Therefore the solution is , , , and .