Matrix Algebra - Example
Solve the system of linear equations, using the matrix methods:
S o l u t i o n
Let's record the given system of linear equations in the matrix form:
The solution of the given system of linear equations in the matrix form looks like:
where – an inverse matrix to a matrix A.
The determinant of the matrix A of coefficients is equal:
consequently, the matrix A has an inverse matrix .
First we’ll find an adjoint matrix Ã which in the given example looks like:
where– algebraic additions of appropriating elementsof matrix A.
In our case we’ll receive:
Then the inverse matrix is equal:
Now we’ll find the solution of the given system of equations. As,then
Thus, the solution of the given system of equations: