Question

Given that P=(2,10)
(5,-3)
a. Evaluate the inverse P^-1, of P
b. use a matrix method to solve x(2,5)+ y(1,-3) =(7,1)

Answer 1

The inverse of matrix A=
a b
c d
is
d -b
-c a
divided by the determinant ad-bc.
So the inverse of
2 10
5 -3
is
-3 -10
-5 2
divided by (-3)(2)-(-5)(-10)=-56, or
3/56 10/56
5/56 -2/56

To find the solution of the given problem, pre-multiply the equation by A^-1 to get
[x,y]=A^-1 [7,1]