Alg2 lesson 4-8
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The document discusses writing and solving systems of equations using matrix form. It explains how to determine the coefficient, variable, and constant matrices and write the corresponding matrix equation. It then provides examples of using the matrix equation to solve systems of equations and discusses what to do when the system has no solution.
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Alg2 lesson 4-8
- 1. A system of equations can be written in matrix form.Determine the coefficient, variable, and constant matrices.Write the matrix equation.A•XB=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.BAXBA-1A-1A=XA-1I=XBA-1=XBExample 8-1b
- 5. A-1=XB
- 6. Use a matrix equation to solve the system of equations.A X = BThe matrix equation isExample 8-3a
- 7. A X = B=A-1=XBAnswer: The solution is (5, –4).Example 8-3b
- 8. Use a matrix equation to solve the system of equations.The matrix equation is whenExample 8-4a
- 9. The determinant of the coefficient matrix is 0,so A–1 does not exist.A-1=XBExample 8-4b
- 10. Graph the system of equations.Since the lines are parallel, thissystem has no solution.Example 8-4c