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# Solving Matrix Equations

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In this lesson, we will learn how to solve a system of linear equations with matrix equations. To do this, we will first write our equations in standard form. Then we will set up three matrices. Once for the coefficients (A), another for the variables (X), and a final matrix (B) for the constants. We can then set up a matrix equation: AX = B. This equation can be solved as: AA

IX = A

X = A

So we find that X, is just the inverse of matrix A or the coefficient matrix multiplied by matrix B, the constant matrix.

^{(-1)}X = A^{(-1)}BIX = A

^{(-1)}BX = A

^{(-1)}BSo we find that X, is just the inverse of matrix A or the coefficient matrix multiplied by matrix B, the constant matrix.

Solving Matrix Equations:

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