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6.1 Solving Systems with Matrices (row reduction)-John Gabriel 1 of 5 Student: John Gabriel Date: 12/10/16 https://xlitemprod.pearsoncmg.com/api/v1/print/math Instructor: Laura Franks Course: College Algebra Fall 2016 Assignment: 6.1 Solving Systems with Matrices (row reduction) 1. Find the augmented matrix for the system. 4x + 8y + 6z = 8x + 4z = 3x + 2y + z = 3 8 9 3 The augmented matrix for the system is 8 . 1 2. 9 xy+z=0 Using Gauss-Jordan elimination to solve the system 4x + y 3z = 17 , the matrix obtained is 2x 4y + 5z = 7 1 0 0 3 0 1 0 2 . Complete the following sentence. 0 0 1 1 The system's solution set is __________. The system's solution set is {( , )}. (Type an ordered triple.) , 3. Write the augmented matrix for the system of linear equations. 3x + y + 6z = 9 5x 8y z = 4 x 9y 6z = 7 Enter the augmented matrix. 4. Write the augmented matrix for the system of equations to the right. x y + 4z = 7 y 10z = 12 z = 2 Enter each element. (Do not simplify.) 12/10/16 11:39 PM 6.1 Solving Systems with Matrices (row reduction)-John Gabriel 2 of 5 5. Write the augmented matrix for the system of equations to the right. https://xlitemprod.pearsoncmg.com/api/v1/print/math 8x y + 8z = 9 5x 9y = 6 9x 2z = 4 Enter each element. (Do not simplify.) 6. Write the augmented matrix for the system of linear equations. 7w w 5w 7. 8x 6x +x 4x 7y +y + 9y 9y + z = 69 = 15 = 34 = 19 Write the system of linear equations represented by the augmented matrix to the right. Use x, y, and z for the variables. 5 0 4 10 0 1 7 3 2 0 13 5 Write the equation represented by the first row. Write the equation represented by the second row. Write the equation represented by the third row. 12/10/16 11:39 PM 6.1 Solving Systems with Matrices (row reduction)-John Gabriel 3 of 5 8. https://xlitemprod.pearsoncmg.com/api/v1/print/math Write the system of linear equations represented by the augmented matrix to the right. Use w, x, y, and z for the variables. 1 5 2 6 3 0 1 2 0 7 0 0 1 1 3 1 5 0 0 3 Write the equation represented by the first row. Write the equation represented by the second row. Write the equation represented by the third row. Write the equation represented by the fourth row. 9. Perform the following matrix row operation and write the new matrix. 3 6 15 21 7 3 4 0 1 0 5 1 1 R 3 1 After performing the row operation, the new matrix is . (Simplify your answer.) 10. Perform the row operation on the given augmented matrix. 1 6 8 3 7 6 2 7 6 5 6 2 7R1 + R2 What is the resultant matrix? 12/10/16 11:39 PM 6.1 Solving Systems with Matrices (row reduction)-John Gabriel 4 of 5 https://xlitemprod.pearsoncmg.com/api/v1/print/math 11. Perform each matrix row operation and write the new matrix. 1 1 1 1 2 0 1 1 9 0 3 0 2 7 2 4 11 3 8 8 3R1 + R3 7R1 + R4 Complete the new matrix below. . 12. Solve the system using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. x+ y z= 4 4x y + z = 4 x + 3y 2z = 1 , The solution set is {( , )}. (Simplify your answers. Type an ordered triple.) 13. Solve the system using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. x + 2y = 0 x + 3y + z = 1 3x y z = 11 , The solution set is {( , )}. (Simplify your answers. Type an ordered triple.) 14. Solve the system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 3x 3y + 4z = 1 5x y 5z = 6 x 3y = 9 The solution set is ( , , ) (Simplify your answers. Type an ordered triple.) 15. Solve the system of equations to the right using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. x+y+z = xyz = 8 xy+z = The solution set is {( , , 4 0 )}. 12/10/16 11:39 PM 6.1 Solving Systems with Matrices (row reduction)-John Gabriel 5 of 5 https://xlitemprod.pearsoncmg.com/api/v1/print/math 16. Solve the system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. x + 7y = z +6 x =2 +y z x +y 3z = 4 The solution set is {( , , )} (Simplify your answers. Type an ordered triple.) 17. Solve the system of equations to the right using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 3a b + 3c = 4 2a b + 5c = 11 a + 2b 3c = 6 , The solution set is {( , )}. 18. Solve the system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. 4x + 4y + 16z = 8 4x + 3y + 14z = 4 4x + 8y + 15z = 33 , The solution set is {( 19. , )}. (Simplify your answers. Type an ordered triple.) Solve the system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. Express the solution set as {(w,x,y,z)}. w + z = 7 3w + 4x + 4y + 2z = 16 3w + x + x 3y 3z = 17 w + 3x + The solution set is {( , , , y + y 3z = 21 )}. (Simplify your answers.) 20. Solve the system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. Express the solution set as {(w,x,y,z)}. 3w + 4x 5y z = w+ x y+ z= 15 7 3w + x y z = 7 w + 2x + 3y 3z = 17 The solution set is {( , , , )}. (Simplify your answers.) 12/10/16 11:39 PM