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Home » Math Homework Help » Algebra Homework Help » Linear Equation Matrix Inverse
Linear Equation Matrix Inverse
We can solve system of linear equations with the help of inverse of a matrix. This method is known as Matrix Inverse Method. The solution of the equations is given by the following method:

Step I: Write down the equations in the form of a single matrix equation

AX = B                               (1)

Where A = co-efficient matrix,

B = constant matrix and

X = variable matrix.

Step II: Find | A |.

Step III: (a) If | A | = 0, then the system of equations has either no solution or have an infinite number of solutions.

(b) If | A | ≠ 0, then the system of equation has a non-zero solution. In that case calculate A-1.

Step IV: Pre-multiplying both sides of the equation (i) by A-1, so that we have

A-1 AX = A-1B

   IX = A-1B or X = A-1B

Step V: Equate the two matrices and then we shall get the values of the variables x, y, z, … of the variable matrix.

Note: A rigorous solution of linear equations is possible by means of rank of a matrix.

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