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4.8 Using matrices to solve systems!

4.8 Using matrices to solve systems!. 2 variable systems – by hand 3 or more variables – using calculator!. Writing systems using matrices. To rewrite a system using matrices 1 st , set up the equations in consistent order (as if you were solving by elimination method)

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4.8 Using matrices to solve systems!

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  1. 4.8 Using matrices to solve systems! 2 variable systems – by hand 3 or more variables – using calculator!

  2. Writing systems using matrices • To rewrite a system using matrices • 1st , set up the equations in consistent order (as if you were solving by elimination method) • 2nd, you need to write 3 matrices: • A coefficient matrix • A variable matrix (this will be a column matrix) • A constant matrix (this will be a column matrix as well) • For example, the system of equations: • 3x + 5y = 19 • 2x – 7y = 13 • Becomes the following matrix equation:

  3. Note that if we multiply the equation back out, we will obtain the original system of equation • To solve the equation, we need to get rid of the coefficient matrix • Do this by multiplying each side on the LEFT by the inverse of the coefficient matrix!

  4. Write a matrix equation for the system of equations. A • X B = Answer: Example 8-1a Determine the coefficient, variable, and constant matrices. Write the matrix equation.

  5. Write a matrix equation for the system of equations. Answer: Example 8-1b

  6. Use a matrix equation to solve the system of equations. The matrix equation when Example 8-3a

  7. Multiply each side by A–1. Example 8-3b Step 1Find the inverse of the coefficient matrix. Step 2Multiply each side of the matrix equation by the inverse matrix.

  8. Multiply matrices. Example 8-3c Answer: The solution is (5, –4). Check this solution in the original equations.

  9. Use a matrix equation to solve the system of equations. Example 8-3d Answer: (2, –4)

  10. Use a matrix equation to solve the system of equations. The matrix equation is when Example 8-4a

  11. The determinant of the coefficient matrix is 0,so A–1 does not exist. Example 8-4b Find the inverse of the coefficient matrix.

  12. Example 8-4c Graph the system of equations. Since the lines are parallel, thissystem has no solution. The system is inconsistent. Answer: There is no solution of this system.

  13. Use a matrix equation to solve the system of equations. Example 8-4d Answer: no solution

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