Question

How can i use an inverse matrix to solve this equation? -x + y= 4, -2x + y = 0

Answer 1

`x,y in { 4,8 }`

Explanation:

`-x+y=4, -2x+y=0`

Rewrite these equations using matrices

`((-1,1),(-2,1))((x),(y))=((4),(0))`

Let `A = ((-1,1),(-2,1))`

Then `A((x),(y))=((4),(0))`

And `((x),(y))=A^-1((4),(0))`

`det(A)=-1(1)-(-2)1=1 rArr A^-1=((1,-4),(2,-1))`

`((x),(y))=((1,-4),(2,-1))((4),(0))=((4),(8))`

`therefore x=4, y=8`

You may have noticed there's another way to do it. From the second equation, we get `y=2x`. Subbing this into the first equation allows us to solve for `x` and `y`