. Using Inverse Matrices to Solve a System: Express the system of linear equations as a matrix equation. Then solve the matrix equation by multiplying each side by the inverse of the coefficient matrix.
The system of a linear equation .
If a square matrix of dimension has an inverse , and if is a variable matrix and is a known matrix both with rows, then the solution of the matrix equation is given by:
Consider the system of equations .
The given system of linear equations can be expressed as a matrix equation as following:
where, , , and .
Inverse of the coefficient matrix, is calculated below:
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