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College Algebra K /DC Tuesday, 29 April 2014

College Algebra K /DC Tuesday, 29 April 2014. OBJECTIVE TSW solve systems of equations using matrices. NEXT TEST ON FRIDAY, 05/02/14 Sec. 5.1, 5.2, and 5.5 Everyone needs a graphing calculator. Solving a System with Infinitely Many Solutions.

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College Algebra K /DC Tuesday, 29 April 2014

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  1. College Algebra K/DCTuesday, 29 April 2014 OBJECTIVETSW solve systems of equations using matrices. NEXT TEST ON FRIDAY, 05/02/14 Sec. 5.1, 5.2, and 5.5 Everyone needs a graphing calculator.

  2. Solving a System with Infinitely Many Solutions • Solve the system. Use y as the arbitrary variable.

  3. Using the Gauss-Jordan Method – 3 Variables The system has the augmented matrix • Solve the system.

  4. Using the Gauss-Jordan Method – 3 Variables There is already a 1 in the first row, first column. Multiply each entry in the first row by –2, then add the result to the corresponding element of the second row to get a 0 in the second row, first column position.

  5. Using the Gauss-Jordan Method – 3 Variables Multiply each entry in the second row by , to get a 1 in the second row, second column position. Multiply each entry in the first row by –3, then add the result to the corresponding element of the third row to get a 0 in the third row, first column position.

  6. Using the Gauss-Jordan Method – 3 Variables Multiply each entry in the third row by , to get a 1 in the third row, third column position. Multiply each entry in the second row by 4, then add the result to the corresponding element of the third row to get a 0 in the third row, second column position.

  7. Using the Gauss-Jordan Method – 3 Variables Multiply each entry in the third row by , then add the result to the corresponding element of the second row to get a 0 in the second row, third column position. Subtract row 2 from row 1 to get a 1 in the first row, second column position.

  8. Using the Gauss-Jordan Method – 3 Variables Multiply each entry in the third row by 4, then add the result to the corresponding element of the first row to get a 0 in the first row, third column position. Verify that (3, –1, –2) satisfies the original system. Solution set: {(3, –1, –2)}

  9. Using the Gauss-Jordan Method: Infinitely Many Solutions • Use the Gauss-Jordan method to solve the system. Write the solution set with z arbitrary. The system has the augmented matrix

  10. Using the Gauss-Jordan Method: Infinitely Many Solutions It is not possible to go further. The equations that correspond to the final matrix are Solve these equations for x and y, respectively Solution set: {(–3z + 18, 5z – 31, z)}

  11. Assignment: Sec. 5.2: pp. 518-519 (25-35 odd, 36-38 all)Due on Friday, 02 May 2014. • Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, give the solution with y arbitrary; for systems in three variables with infinitely many solutions, give the solution with z arbitrary.

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