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Quiz: Elementary matrices

Page history last edited by Issa Rice 1 year, 7 months ago

This quiz is designed to test basic concepts concerning matrices and vectors.

 

Discuss this quiz 

(Key: correct, incorrect, partially correct.)

 

  1. Let Formula be an Formula matrix, and let Formula be a Formula matrix. Which of the four operations Formula, Formula, Formula, Formula make sense?
    1. Formula and Formula make sense.
      • CORRECT.
    2. Formula and Formula make sense.
    3. None of the operations make sense.
    4. Formula makes sense.
    5. All of the operations make sense.
    6. Formula makes sense.
    7. Formula makes sense.
  2. Let Formula be an Formula matrix, and let Formula be a Formula matrix. Which of the four operations Formula, Formula, Formula, Formula make sense?
    1. Formula and Formula make sense.
    2. Formula and Formula make sense.
    3. None of the operations make sense.
    4. Formula makes sense.
      • CORRECT.
    5. All of the operations make sense.
    6. Formula makes sense.
    7. Formula makes sense.
  3. Let Formula be an Formula matrix, and let B be a Formula matrix. Which of the four operations Formula, Formula, Formula, Formula make sense?
    1. Formula and Formula make sense.
    2. Formula and Formula make sense.
      • CORRECT.
    3. None of the operations make sense.
    4. Formula makes sense.
    5. All of the operations make sense.
    6. Formula makes sense.
    7. Formula makes sense.
  4. Let Formula be an Formula matrix, and let B be a Formula matrix. Which of the four operations Formula, Formula, A + B, A - B make sense?
    1. Formula and Formula make sense.
    2. Formula and Formula make sense.
    3. None of the operations make sense.
    4. Formula makes sense.
    5. All of the operations make sense.
      • CORRECT.
    6. Formula makes sense.
    7. Formula makes sense.
  5. If one multiplies a row vector by a column vector, one gets
    1. Nothing; this operation cannot be defined in general.
    2. A number, if the two vectors have the same length, and nothing (undefined) otherwise.
      • CORRECT.
    3. A number.
    4. A matrix.
    5. A row vector.
    6. A column vector.
    7. An L-shaped vector.
  6. If one adds a row vector to a column vector, one gets
    1. Nothing; this operation cannot be defined in general.
      • CORRECT.
    2. A number, if the two vectors have the same length, and nothing (undefined) otherwise.
    3. A number.
    4. A matrix.
    5. A row vector.
    6. A column vector.
    7. An L-shaped vector.
  7. If one multiplies a matrix with a column vector, one gets
    1. Nothing; this operation cannot be defined in general.
    2. A column vector, if the number of columns of the matrix matches the number of rows of the vector.
      • CORRECT.
    3. A column vector, if the number of rows of the matrix matches the number of columns of the vector.
    4. A column vector, if the number of rows of the matrix matches the number of rows of the vector.
    5. A matrix.
    6. A row vector.
    7. A number.
  8. If one multiplies a column vector with a row vector, one gets
    1. Nothing; this operation cannot be defined in general.
    2. A column vector, if both vectors have the same length.
    3. A row vector, if both vectors have the same length.
    4. A column vector, in all cases.
    5. A matrix.
      • CORRECT.
    6. A row vector, in all cases.
    7. A number.
  9. If one multiplies a column vector with a matrix, one gets
    1. Nothing; this operation cannot be defined in general.
      • CORRECT.
    2. A column vector, if the number of columns of the matrix matches the number of rows of the vector.
    3. A column vector, if the number of rows of the matrix matches the number of columns of the vector.
    4. A column vector, if the number of rows of the matrix matches the number of rows of the vector.
    5. A matrix.
    6. A row vector.
    7. A number.
  10. Let Formula be a matrix. Under what conditions will Formula will make sense?
    1. Formula must be a square matrix.
      • CORRECT.
    2. Formula must have at least as many rows as columns.
    3. Formula must have at least as many columns as rows.
    4. Formula must be a row vector.
    5. Formula must be a column vector.
    6. Formula makes sense for any matrix Formula.
    7. Formula must be in reduced row-echelon form.
  11. If Formula is a Formula matrix, then the determinant of Formula is
    1. A Formula matrix.
    2. Formula number (possibly non-zero).
    3. Zero.
    4. Undefined.
      • CORRECT.
    5. A Formula matrix.
    6. A subspace of Formula.
    7. A subspace of Formula.
  12. If Formula is a Formula matrix, then the rank of Formula is
    1. A Formula matrix.
    2. A number (possibly non-zero).
      • CORRECT.
    3. Zero.
    4. Undefined.
    5. A Formula matrix.
    6. A subspace of Formula.
    7. A subspace of Formula.
  13. If Formula is a Formula matrix, then the transpose of Formula is
    1. A Formula matrix.
    2. A number (possibly non-zero).
    3. Zero.
    4. Undefined.
    5. A Formula matrix.
      • CORRECT.
    6. A subspace of Formula.
    7. A subspace of Formula.
  14. If Formula is a Formula matrix, then the inverse of Formula is
    1. A Formula matrix.
    2. A number (possibly non-zero).
    3. Zero.
    4. Undefined.
      • CORRECT. Only square matrices can be invertible.
    5. A Formula matrix.
    6. A subspace of Formula.
    7. A subspace of Formula.
  15. If Formula is a Formula matrix, then the image of Formula is
    1. A Formula matrix.
    2. A number (possibly non-zero).
    3. Zero.
    4. Undefined.
    5. A Formula matrix.
    6. A subspace of Formula.
      • CORRECT.
    7. A subspace of Formula.
  16. If Formula is a Formula matrix, then the kernel of Formula is
    1. A Formula matrix.
    2. A number (possibly non-zero).
    3. Zero.
    4. Undefined.
    5. A Formula matrix.
    6. A subspace of Formula.
    7. A subspace of Formula.
      • CORRECT.
  17. If Formula is a Formula matrix, then the row-reduced echelon form of Formula is
    1. A Formula matrix.
      • CORRECT.
    2. A number (possibly non-zero).
    3. Zero.
    4. Undefined.
    5. A Formula matrix.
    6. A subspace of Formula.
    7. A subspace of Formula.
      • CORRECT.

 

 

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