Please help with one math problem about matrix inverses
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Please help with one math problem about matrix inverses

[From: ] [author: ] [Date: 11-11-21] [Hit: ]
,?I just started learning the concept, this problem is too hard to me no matter how many times I tried, please help out, thanks-Recall that in order to solve the equation Ax = b,......
Use the method of matrix inverses to solve the system.
(5/2)x+(1/6)y= -13
(1/3)x-(1/4)y= -5

(x, y) =(?,?)
I just started learning the concept, this problem is too hard to me no matter how many times I tried, please help out, thanks

-
Recall that in order to solve the equation Ax = b, we can take the inverse of both sides:

x = (A^-1)b

For a 2 by 2 matrix with entries a and b in the first row and c and d in the second row, the inverse can be found by doing:

A^-1 = 1/(ad - bc) * [d -b, c -a] where the comma represents the next row in the inverse.

So, in this case our b vector is [-13 -5]^(T) where T means transpose and our A matrix is simply:

A = [5/2 1/6 , 1/3 -1/4]

So A^-1 = 1/(-5/8 - 1/18) * [-1/4 -1/6, 1/3 -5/2] = [18/49 12/49, -24/49 180/49]

x which is the solution vector = A^-1 * b = [18/49 12/49, -24/49 180/49] * [-13 -5]^(T)

x = [-6 , -12]

I made a mistake somewhere along here since when plugged back in, my solution doesn't seem to work. You can probably find it and correct it.
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