Math Tutoring on Using The Matrix Equation
A system of equations can also be solved by Matrix Method. This Matrix Method of solving systems of equations involves expressing the system of equations in the form of a matrix and then reducing that matrix in Row Echelon Form. The Matrix Equation:
AX = B
A-1AX = A-1B
InX = A-1B
X = A-1B
We can solve the system using LU Decomposition, where L is a lower triangular matrix and U is an upper triangular matrix.
Let A = LU and substitute into AX = B.
We have to now solve LUX = B for X to solve the system.
Let UX = Y,
then, LY = B and UX = Y
Now we first solve LY = B for Y and then solve UX = Y for X.
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