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Matrices Homework -- Homework: Determinants

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems related to determinants.

Exercise 1

| 3 4 5 6 | | 3 4 5 6 |

  • a. Find the determinant by hand.
  • b. Find the determinant by using your calculator.
  • c. Finally, use your calculator to find the determinant of the inverse of this matrix.

hint:

You should not have to type in the inverse by hand.

What did you get? Can you make a generalization about the "determinant of an inverse matrix"?

Exercise 2

| 1 2 3 n | = 2 | 1 2 3 n |=2

  • a. What is nn?
  • b. Check your answer by using your calculator.

Exercise 3

|24613n579|=|24613n579| size 12{ lline matrix { 2 {} # 4 {} # 6 {} ## 1 {} # 3 {} # n {} ## 5 {} # 7 {} # 9{} } rline } {}=

Exercise 4

| 2 4 6 1 3 8 5 7 9 | | 2 4 6 1 3 8 5 7 9 size 12{ lline matrix { 2 {} # 4 {} # 6 {} ## 1 {} # 3 {} # 8 {} ## 5 {} # 7 {} # 9{} } rline } {} |

  • a. Find the determinant by hand.
  • b. Find the determinant by using the formula you found in #3.
  • c. Find the determinant by using your calculator.

Exercise 5

A triangle has vertices at (-1,-2), (1,5), and (3,4).

  • a. Do a quick sketch of the triangle.
  • b. Set up a determinant that will find its area.
  • c. Evaluate that determinant (use your calculator) to find the area.
  • d. Can you think of any other way to find the area of this triangle?

Exercise 6

Use your calculator to find the determinant | 1342653895974120||1342653895974120 size 12{ lline matrix { 1 {} # 3 {} # 4 {} # 2 {} ## 6 {} # 5 {} # 3 {} # 8 {} ## 9 {} # 5 {} # 9 {} # 7 {} ## 4 {} # 1 {} # 2 {} # 0{} } rline } {}|.

Exercise 7

Make up a 3×3 matrix whose determinant is zero. (Do not use all zeros!) Try to find its inverse on your calculator. What happens?

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