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4.5 Solving Systems using Matrix Equations and Inverses

4.5 Solving Systems using Matrix Equations and Inverses. Matrix Equation. A linear system can be written as a matrix equation AX=B. Constant matrix. Coefficient matrix. Variable matrix. Ex. 1 Write as a matrix equation. Solving Matrix Equations. Suppose ax = b How do you solve for x?.

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4.5 Solving Systems using Matrix Equations and Inverses

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  1. 4.5Solving Systems using Matrix Equations and Inverses

  2. Matrix Equation A linear system can be written as a matrix equation AX=B Constant matrix Coefficient matrix Variable matrix

  3. Ex. 1 Write as a matrix equation.

  4. Solving Matrix Equations Suppose ax = b How do you solve for x? We cannot divide matrices, but we can multiply by the inverse. A-1 AX = B A-1 IX = A-1B X = A-1B

  5. Ex. 2 Solve using matrices. AX = B X = A-1B x = -7 y = -4 B A (-7, -4)

  6. Ex. 3 Solve using matrices x = 5/7 y = 2 (5/7, 2)

  7. Ex. 4 Solve using matrices x = 2 y = -1 z = -2 (2, -1, -2)

  8. Ex. 5 Solve using matrices x = 4 y = -7 z = 2 (4, -7, 2)

  9. Assignment

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