How to Solve a System of Linear Equations Using Inverse Matrices


This is a simple guide to solving a 2x2 matrix using the inverse method.

Steps

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    Write the equations as a matrix. Label each matrix as A, X, and C.
    • If A times X equals C, then A^-1 (the inverse of A) times A times X equals A^-1 times C, then X equals A^-1 times C. This is because A and its inverse cancel each other out.
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    Find the opposite matrix, which is a and d switched, and then the signs switched on b and c.
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    Find the inverse matrix. To do this, you need to solve for 1 over ab-cd times the opposite matrix.
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    Take the inverse matrix and multiply the x and y columns by x and y, respectively. That will give you your answer.

Article Info

Categories: Merge | Mathematics