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Quiz: Determinants

Page history last edited by Jeb 10 years, 4 months ago

This quiz is designed to test basic properties of determinants.

 

Discuss this quiz 

(Key: correct, incorrect, partially correct.)

 

  1. Let Formula be a Formula matrix with determinant 6. What is the determinant of Formula (the inverse of Formula)?
    1. 1/6.
      • CORRECT.
    2. 6.
    3. 0.
    4. 30.
    5. 25/6.
    6. 1.
    7. Insufficient information to solve the question.
  2. Let Formula be a Formula matrix with determinant Formula, and let Formula be a Formula matrix with determinant 4. What is the determinant of Formula?
    1. 24.
      • CORRECT.
    2. 10.
    3. 0.
    4. 1/6.
    5. 1/4.
    6. 1.
    7. Insufficient information to solve the question.
  3. Let Formula be a Formula matrix with determinant 6, and let Formula be a Formula matrix with determinant 4. What is the determinant of A+B?
    1. 24.
    2. 10.
    3. 0.
    4. 1/6.
    5. 1/4.
    6. 1.
    7. Insufficient information to solve the question.
      • CORRECT.
  4. Let Formula be a Formula matrix with determinant 3. What is the determinant of -A?
    1. 3.
      • CORRECT.
    2. -3.
    3. 1/3.
    4. 0.
    5. 1.
    6. -1.
    7. Insufficient information to solve the question.
  5. Let Formula be a Formula matrix with determinant 3. What is the determinant of 2A?
    1. 48.
      • CORRECT.
    2. 6.
    3. 3.
    4. 24.
    5. 12.
    6. 196,608.
    7. Insufficient information to solve the question.
  6. Let Formula be a Formula matrix with determinant 3. What is the determinant of A^t (the transpose of Formula)?
    1. 3.
      • CORRECT.
    2. 3^t.
    3. 12.
    4. 1/3.
    5. 27.
    6. 81.
    7. Insufficient information to solve the question.
  7. Let Formula be a Formula matrix with determinant 3. Let Formula be the matrix formed by swapping the second and third rows of Formula. What is Formula?
    1. -3.
      • CORRECT.
    2. 3.
    3. 0.
    4. 1/3.
    5. 6.
    6. 2.
    7. Insufficient information to solve the question.
  8. Let Formula be a Formula matrix with determinant 3. Let Formula be the matrix formed by multiplying the fourth row of Formula by 2. What is Formula?
    1. 6.
      • CORRECT.
    2. 3.
    3. 3/2.
    4. -48.
    5. 48.
    6. -6.
    7. Insufficient information to solve the question.
  9. Let Formula be a Formula matrix with determinant 3. Let Formula be the matrix formed by dividing the fourth row of Formula by 2. What is Formula?
    1. 3/2.
      • CORRECT.
    2. 3.
    3. 6.
    4. 3/16.
    5. 3/4.
    6. -3.
    7. Insufficient information to solve the question.
  10. Let Formula be a Formula matrix with determinant 3. Let Formula be the matrix formed by adding two copies of the third row to the first. What is Formula?
    1. 3.
      • CORRECT.
    2. 6.
    3. 0.
    4. -3.
    5. -6.
    6. 9.
    7. Insufficient information to solve the question.
  11. Let Formula be a Formula matrix with determinant 3. Let Formula be the matrix formed by subtracting two copies of the third row from the first. What is Formula?
    1. 3.
      • CORRECT.
    2. 6.
    3. 0.
    4. -3.
    5. -6.
    6. -9.
    7. Insufficient information to solve the question.
  12. Let Formula be a Formula matrix. The relationship between determinant and invertibility is
    1. Formula is invertible if and only if its determinant is non-zero.
      • CORRECT.
    2. Formula is invertible if its determinant is non-zero, but not conversely.
    3. The determinant of Formula is non-zero if Formula is invertible, but not conversely.
    4. Formula is invertible if and only if its determinant is zero.
    5. Formula is invertible if its determinant is zero, but not conversely.
    6. The determinant of Formula is zero if Formula is invertible, but not conversely.
    7. There is no connection between the two concepts.

 

 

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