# Solution To Linear System By Inverse Method

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**Solution to Linear System by Inverse Method:**

If A is an n n matrix then the linear system AX = B is a system of n equations in m unknown. Suppose that A is a non-singular. Then A^{-1} exists and we can multiply,

** AX = B
**

By A^{-1 }on the both side we get;

Moreover, X = A^{-1}B is clearly solution to the given linear system. If A is nonsingular, we have a unique solution;

**Example-** Consider the system

The matrix operation corresponding to the system is;

**Example-** Consider the system

Then,