Exam. Name. Solve the system of equations by graphing. 1) 2x y 5 3x y 6. Solve the system of equations by substitution.

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1 Exam Name Solve the system of equations by graphing. 1) 2x y 5 3x y 6 10 y 1) x Var: 50 Objective: (4.1) Solve Systems of Linear Equations by Graphing Solve the system of equations by substitution. 2) x 4y 4 9x 3y 3 Var: 50 Objective: (4.1) Solve Systems of Linear Equations Using Substitution 2) Solve the system of equations by elimination. 3) x 5y 35 5x 4y 28 Objective: (4.1) Solve Systems of Linear Equations Using Elimination by Addition 3) Solve the problem. 4) Daisy has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of $4.35, how many of the coins are nickels? Objective: (4.1) Solve Applications 5) A company that manufactures laser printers for computers has monthly fixed costs of $177,000 and variable costs of $650 per unit produced. The company sells the printers for $1,250 per unit. How many printers must be sold each month for the company to break even? Objective: (4.1) Solve Applications 4) 5) 9

2 Provide an appropriate response. 6) Given matrix A: A What is the size of A? 7) Write the augmented matrix for the system. 8x1 9x x1 6x2 66 6) 7) 8) Given matrix A: A 0 2 8) What is the size of A? Find a32 and a11. Perform the indicated row operations on the following matrix ) 3R1 R1 9) Objective: (4.2) Perform Row Operations Identify the row operation that produces the resulting matrix ) Objective: (4.2) Identify Row Operations 10) Write a system of equations associated with the augmented matrix. Do not try to solve ) Objective: (4.2) Solve Systems of Linear Equations Using Augmented Matrix Methods 11) 10

3 Provide an appropriate response. 12) Solve the linear system corresponding to the following augmented matrix: Objective: (4.2) Solve Systems of Linear Equations Using Augmented Matrix Methods 12) State whether the matrix is in reduced form or not in reduced form ) Objective: (4.3) Determine Whether Matrices Are in Reduced Form 13) Write the linear system corresponding to the reduced augmented matrix ) Objective: (4.3) Write Linear Systems Corresponding to Reduced Augmented Matrix 14) User row operations to change the matrix to reduced form ) Objective: (4.3) Use Row Operations to Change Matrices to Reduced Form 15) Solve using GaussJordan elimination. 16) 2x 4y 2 2x 5y 4 Var: 50 Objective: (4.3) Solve Systems of Linear Equations Using GaussJordan Elimination 16) 17) x y z 7 x y 3z 11 5x y z 11 Var: 50 Objective: (4.3) Solve Systems of Linear Equations Using GaussJordan Elimination 17) Perform the operation, if possible. 18) Objective: (4.4) Add or Subtract Matrices 18) 19) ) Objective: (4.4) Add or Subtract Matrices 11

4 20) Let C and D Objective: (4.4) Find Products of Numbers and Matrices 21) A , B Var: 27 Objective: (4.4) Find Matrix Products 22) Let A and B. Find C 4D. 20) Find BA. 21). Find AB. 22) Objective: (4.4) Find Matrix Products Find the matrix product mentally, without the use of a calculator or pencilandpaper calculations. 23) Objective: (4.5) Find Matrix Products Mentally 23) Determine whether B is the inverse of A ) A 1 1 2, B Objective: (4.5) Determine Whether Matrices Are Inverses of One Another 24) Find the inverse, if it exists, of the given matrix. 25) Var: 8 Objective: (4.5) Find Matrix Inverses 25) 26) Objective: (4.5) Find Matrix Inverses 26) 12

5 Answer Key Testname: FINITE TEST 2 PRACTICE 1) (1, 3) ID: FM12B Objective: (4.1) Solve Systems of Linear Equations by Graphing 2) (0, 1) ID: FM12B Objective: (4.1) Solve Systems of Linear Equations Using Substitution 3) (0, 7) ID: FM12B Objective: (4.1) Solve Systems of Linear Equations Using Elimination by Addition 4) 7 nickels ID: FM12B Objective: (4.1) Solve Applications 5) 295 printers per month ID: FM12B Objective: (4.1) Solve Applications 6) 2 3 ID: FM12B ) ID: FM12B ) 4 2; a32 2; a ) ID: FM12B ID: FM12B Objective: (4.2) Perform Row Operations 10) R1 R2 R2 ID: FM12B Objective: (4.2) Identify Row Operations 11) 3x1 3x2 5x3 2 5x1 7x3 4 3x1 6x2 2 ID: FM12B Objective: (4.2) Solve Systems of Linear Equations Using Augmented Matrix Methods 13

6 Answer Key Testname: FINITE TEST 2 PRACTICE 12) (2, 5) ID: FM12B Objective: (4.2) Solve Systems of Linear Equations Using Augmented Matrix Methods 13) Not Reduced Form ID: FM12B Objective: (4.3) Determine Whether Matrices Are in Reduced Form 14) x1 4, x2 0 15) ID: FM12B Objective: (4.3) Write Linear Systems Corresponding to Reduced Augmented Matrix ID: FM12B Objective: (4.3) Use Row Operations to Change Matrices to Reduced Form 16) (3, 2) ID: FM12B Objective: (4.3) Solve Systems of Linear Equations Using GaussJordan Elimination 17) (1, 2, 4) ID: FM12B Objective: (4.3) Solve Systems of Linear Equations Using GaussJordan Elimination 18) ID: FM12B Objective: (4.4) Add or Subtract Matrices 19) Not defined ID: FM12B Objective: (4.4) Add or Subtract Matrices 20) ID: FM12B Objective: (4.4) Find Products of Numbers and Matrices 21) AB is not defined. ID: FM12B Objective: (4.4) Find Matrix Products 22) ID: FM12B Objective: (4.4) Find Matrix Products 14

7 Answer Key Testname: FINITE TEST 2 PRACTICE 23) ID: FM12B Objective: (4.5) Find Matrix Products Mentally 24) No ID: FM12B Objective: (4.5) Determine Whether Matrices Are Inverses of One Another 25) 26) ID: FM12B Objective: (4.5) Find Matrix Inverses ID: FM12B Objective: (4.5) Find Matrix Inverses 15

8 Exam Name 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 16

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