You may use a calculator for the entire test; however, the solutions for numbers 1 through 3 must be exact solutions—NO DECIMAL SOLUTIONS FOR THE FIRST PAGE. Do not rationalize. SHOW WORK !
I. Solve the following systems by either the substitution or the elimination (addition) method. Write your answers as ordered pairs/ordered triples.(These are worth 5 points each)
For #3, Solve the system using Cramer’s rule and Algebra. SHOW THE DETERMINANTS and give your solution as a simplified ORDERED PAIR. (exact solutions only). These are worth 4 points each.
Cramer’s ruleSubstitution and/or Elimination
II. Solve the following system by graphing, using the grid provided. (5 points)
-99060-698500 III. Part III tests your ability to use the calculator. You should solve the system by the methods indicated, evaluate the determinants, find the inverse, or perform the matrix arithmetic. Some may be easier to work without the calculator. Give exact answers; give no decimal approximations! If a particular operation is not possible or is undefined, then state the appropriate reason—no work is necessary.
For #5, solve the system using row reduced echelon form or matrix algebra and the inverse matrix. Show the matrices that you put into the calculator and the calculator’s display that yields the solution. Lastly, write the exact value of the ordered triple. (3 pts)
For #6, perform the matrix arithmetic. Only the final answer is required. (1 point.)
For # 7 and #8, evaluate or simplify the expressions. Only the final answers are required. (1 point each.) 7. 8. =
For #9, simplify. (1 point.)
For #10, multiply. (1 point.)