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kenneyfamily
how would you solve the following system using an inverse matrix? 4x - y = 1 x + 2y = 7
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
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