Solving Linear Systems of Equations - Inverse Matrix Consider the following system of equations ... Let the matrix A represent the coefficients ... Let matrix B hold the constants ... Finally, let matrix X represent the variables ...

Solving Linear Systems of Equations - Inverse Matrix Now notice what the result is when we work out the following matrix equation ... Slide 2

Solving Linear Systems of Equations - Inverse Matrix Thus, AX = B represents the system of equations. This matrix equation can be solved for X as follows ... Recall that matrix multiplication is not commutative, so each side of the equation must be multiplied on the left by A-1 Matrix multiplication is associative. Slide 3

Solving Linear Systems of Equations - Inverse Matrix Method of solution: (1) Given a system of equations, form matrices A, X, and B. A Coefficients X Variables (vertical matrix) B Constants (vertical matrix) (2) Find A-1. (3) Find the solution by multiplying A-1 times B. X = A-1 B Slide 4

Solving Linear Systems of Equations - Inverse Matrix Example: Use an inverse matrix to solve the system at the right. Using the methods of finding an inverse, A-1 is ... Slide 5

Solving Linear Systems of Equations - Inverse Matrix Now find X ... The solution is (2, -1), or x = 2 y = -1 Slide 6

Solving Linear Systems of Equations - Inverse Matrix This same method can be used on any size system of equations as long as the coefficient matrix is square and the solution is unique. Slide 7

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