Business Math MATH 1324

North Lake College

David Katz, instructor

Section by Section List of Test Topics For Exam #3 (Chapters 3 and 4)

The exam will consist of 11 free response questions from this list of 32 topics from your homework sections.

This unit focuses on certain types of business applications: investments, resource allocation, revenue, profit, etc. Review these types of word problems in the homework when studying for this exam. There will be 3-4 word problems on the test.

  1. (3-1) Know when matrix addition and subtraction is defined (both matrices must have dimensions n x m)

  2. (3-1) Add or subtract two matrices
  3. (3-1) Multiply a matrix by a scalar (constant)
  4. (3-1) Identify an element of a matrix by the appropriate subscripts (e.g., a12 or b43, etc.)
  5. (3-1) Translate a word problem into matrices using matrix addition, subtraction, and/or scalar multiplication
  6. (3-2) Know when matrix multiplication is defined (If the first matrix is n x m, then the second must be m x p)
  7. (3-2) Describe the dimensions of the product of matrix multiplication before multiplying (n x m by m x p => n x p) 
  8. (3-2) Know that matrix multiplication is not commutative (i.e., [A] x [B] does not always = [B] x [A])
  9. (3-2) Translate a word problem into matrices using multiplication of matrices
  10. (3-3) Write an n x n identity matrix using rows of 1s and 0s in the appropriate places
  11. (3-3) Know that inverse matrices are only possible for square matrices (n x n)
  12. (3-3) Square matrices that do not have inverses are called singular matrices
  13. (3-3) Use augmented matrices and the technique of reduced row echelon form to compute an inverse matrix by hand
  14. (3-3) Use your calculator to compute the inverse of a matrix
  15. (3-3) Know that in this section, [A] refers to a square matrix for the coefficients of a system
  16. (3-3) Know that in this section, [X] refers to a column matrix for the variables of a system
  17. (3-3) Know that in this section, [B] refers to a column matrix for the constants of a system
  18. (3-3) Write a system of equations as a system of matrices of the form [A][X] = [B]
  19. (3-3) Use inverse matrices to solve systems of matrices of the form [A][X] = [B]
  20. (3-3) Translate a word problem into a system of matrices of the form [A][X] = [B]
  21. (4-1) Graph the feasible region (solution set) to a system of linear inequalities
  22. (4-1) Shade the feasible region appropriately so that it can be easily identified
  23. (4-1) Know that some solution sets are bounded; others are unbounded
  24. (4-1) Know when to use a solid line or dashed line when graphing the solution set
  25. (4-1) Give the exact coordinates for all corner points (vertices) of the solution set on the graph
  26. (4-1) Label all essential parts of your graph: corner points, axes, lines, feasible region, etc.
  27. (4-2) Know the Fundamental Theorem of Linear Programming (p.205)
  28. (4-2) Optimal solutions can be found at the corner points for bounded feasible regions
  29. (4-2) Identify the objective function (usually a profit or cost function) for a system of linear inequalities
  30. (4-2) Decide if you have to minimize or maximize the objective function
  31. (4-2) Test the corner points to look for minimum or maximum values of the objective function
  32. (4-2) Translate a word problem into a system of inequalities with an objective function

 

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