Solving system of simulateous linear equations
Consider system of simulateous linear equations in in x ,y ,z
\[a_1x+b_1y+c_1z=d_1\]
\[a_2x+b_2y+c_2z=d_2\]
\[a_3x+b_3y+c_3z=d_3\]
Matrix A can be defined as \[ \begin{bmatrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{bmatrix}\]
and B=\[\begin{bmatrix}d_1\\d_2\\d_3\end{bmatrix}\]
Then solution of system of equation can be written as
AX=B
pre multipling both sides by \[A^{-1}\]
We get \[A^{-1}AX=A^{-1}B\]
Which is equal to \[X=A^{-1}B\] since \[A^{-1}A\] is an identity matrix.
