Solve the following system of linear equations, using matrix method
5x−2y=3,3x+2y=5
The given system can be written as AX=B, where
A=[5232],X=[xy]and B=[35] Here,|A|=[5232]=10−6=4≠0,
Thus, A is non-singular, Therefore, its inverse exists.
Therefore, the given system is consistent and has a unique solution given by X=A−1B.
Cofactors of A are,
A11=2,A12=−3,A21=−2,A22=5adj(A)=[2−3−25]T=[2−2−35]∴A−1=1|A|(adjA)=14[2−2−35]
Now, X=A−1B=14[2−2−35][35]=14[6−10−9+25]=14[−416]=[−14]
⇒[xy]=[−14], Hence, x =-1 and y=4