To solve the given matrix equation, we set up
Ax=B
where
A=[[6,-1],[-2,2]]
B=[2,16]
To solve for x, premultiply by the inverse of A
x=A^(-1)B
The inverse of A can be found as
A^(-1) = [[2,1],[2,6]]/(6*2-(-1)(-2)) [2,16]
=[[2,1],[2,6]]/10 [2,16]
=[[0.2,0.1],[0.2,0.6]] [2,16]
Verify the solution by matrix multiplication:
x=0.2*2+0.1*16=2
y=0.2*2+0.6*16=10
substitute into original equation,
6x-y=12-10=2 ok
-2x+2y=-4+20=16 ok.
It will be your duty as a student to find the right option from the answer.
