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  • 1. A system of equations can be written in matrix form.
    Determine the coefficient, variable, and constant matrices.
    Write the matrix equation.
    A

    X
    B
    =
    Answer:
    Example 8-1a
  • 2. Why does it work???
    Example 8-1a
  • 3. Write a matrix equation for the system of equations.
    Answer:
    Example 8-1b
  • 4. Use the matrix equation to solve the system of equations.
    B
    A
    X
    B
    A-1
    A-1
    A
    =
    X

    A-1
    I
    =
    X
    B

    A-1
    =
    X
    B
    Example 8-1b
  • 5. A-1
    =
    X
    B
  • 6. Use a matrix equation to solve the system of equations.
    A  X = B
    The matrix equation is
    Example 8-3a
  • 7. A  X = B
    =
    A-1
    =
    X
    B
    Answer: The solution is (5, –4).
    Example 8-3b
  • 8. Use a matrix equation to solve the system of equations.
    The matrix equation is when
    Example 8-4a
  • 9. The determinant of the coefficient matrix is 0,so A–1 does not exist.
    A-1
    =
    X
    B
    Example 8-4b
  • 10. Graph the system of equations.
    Since the lines are parallel, thissystem has no solution.
    Example 8-4c