If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
2X+3Y=
-----(i)
= 3X+2Y
-----(ii)
Multiply equation(i) by 3 and equation(ii) by 2, we get,
= 6X+9Y=
= 6X+4Y=
Subtract these equation then we get,
= 5Y=
= 5y=
= 5Y=
= Y=
= Y=
Now, put the value of Y in equation (i)
= 2X+3
= 2X=
-
= 2X=
= 2X=
= X=
= X=
Hence, Y=
and X=
20