Question

how would you solve the following system using an inverse matrix?

4x - y = 1
x + 2y = 7

Answer 1

You can turn this system of equations into matrices.
A=[4 -1;
1 2]
and
b=[1;
7]
And your unknowns will be:
u = [x,
y]
What you have then is:
Au=b
To solve for the unknowns, you would PRE-multiply both sides times the inverse of A

inv(A)*A*u=inv(A)*b
Identity*u=inv(A)*b
u=inv(A)*b

Answer 2

fyi, since:
\[inv(A)=\left[\begin{matrix}2/9 & 1/9 \\ -1/9 & 4/9\end{matrix}\right]\]
you have:
\[\left[\begin{matrix}2/9 & 1/9 \\ -1/9 & 4/9\end{matrix}\right]\left(\begin{matrix}1 \\ 7\end{matrix}\right)\]=\[\left[ \left(\begin{matrix}1 \\ 3\end{matrix}\right) \right]\]
Which means:
x=1 and
y=3

Answer 3

awesome thanks!!!