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Solving Linear Systems of Equations - Inverse Matrix

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.

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Solving Linear Systems of Equations - Inverse Matrix

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  1. 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 ...

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

  3. 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

  4. 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

  5. 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

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

  7. 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

  8. Solving Linear Systems of Equations - Inverse Matrix END OF PRESENTATION Click to rerun the slideshow.

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