# Matrix Equations Step 1: Write the system as a matrix equation. A three-equation system is shown below.

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Matrix Equations Step 1: Write the system as a matrix equation. A three-equation system is shown below.

Matrix Equations Step 2: Find the inverse of the coefficient matrix. Note: This can be done easily for a 2 x 2 matrix. For larger matrices, use a calculator to find the inverse.

Matrix Equations Step 3: Multiply both sides of the matrix equation by the inverse. The inverse of the coefficient matrix times the coefficient matrix equals the identity matrix. Note: The multiplication order on the right side is very important. We cannot multiply a 3 x 1 times a 3 x 3 matrix!

Matrix Equations Example: Solve the system 3x - 2y = x + 2y = -5

Matrix Equations Example, continued: Multiply the matrices (a ‘2 x 2’ times a ‘2 x 1’) first, then distribute the scalar.

Matrix Equations Example #2: Solve the 3 x 3 system 3x - 2y + z = 9 x + 2y - 2z = -5 x + y - 4z = -2 Using a graphing calculator,

Matrix Equations Example #2, continued

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