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# Quiz: Elementary matrices

last edited by 2 years ago

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

Discuss this quiz

(Key: correct, incorrect, partially correct.)

1. Let be an matrix, and let be a matrix. Which of the four operations , , , make sense?
1. and make sense.
• CORRECT.
2. and make sense.
3. None of the operations make sense.
4. makes sense.
5. All of the operations make sense.
6. makes sense.
7. makes sense.
2. Let be an matrix, and let be a matrix. Which of the four operations , , , make sense?
1. and make sense.
2. and make sense.
3. None of the operations make sense.
4. makes sense.
• CORRECT.
5. All of the operations make sense.
6. makes sense.
7. makes sense.
3. Let be an matrix, and let B be a matrix. Which of the four operations , , , make sense?
1. and make sense.
2. and make sense.
• CORRECT.
3. None of the operations make sense.
4. makes sense.
5. All of the operations make sense.
6. makes sense.
7. makes sense.
4. Let be an matrix, and let B be a matrix. Which of the four operations , , A + B, A - B make sense?
1. and make sense.
2. and make sense.
3. None of the operations make sense.
4. makes sense.
5. All of the operations make sense.
• CORRECT.
6. makes sense.
7. 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 be a matrix. Under what conditions will will make sense?
1. must be a square matrix.
• CORRECT.
2. must have at least as many rows as columns.
3. must have at least as many columns as rows.
4. must be a row vector.
5. must be a column vector.
6. makes sense for any matrix .
7. must be in reduced row-echelon form.
11. If is a matrix, then the determinant of is
1. A matrix.
2. number (possibly non-zero).
3. Zero.
4. Undefined.
• CORRECT.
5. A matrix.
6. A subspace of .
7. A subspace of .
12. If is a matrix, then the rank of is
1. A matrix.
2. A number (possibly non-zero).
• CORRECT.
3. Zero.
4. Undefined.
5. A matrix.
6. A subspace of .
7. A subspace of .
13. If is a matrix, then the transpose of is
1. A matrix.
2. A number (possibly non-zero).
3. Zero.
4. Undefined.
5. A matrix.
• CORRECT.
6. A subspace of .
7. A subspace of .
14. If is a matrix, then the inverse of is
1. A matrix.
2. A number (possibly non-zero).
3. Zero.
4. Undefined.
• CORRECT. Only square matrices can be invertible.
5. A matrix.
6. A subspace of .
7. A subspace of .
15. If is a matrix, then the image of is
1. A matrix.
2. A number (possibly non-zero).
3. Zero.
4. Undefined.
5. A matrix.
6. A subspace of .
• CORRECT.
7. A subspace of .
16. If is a matrix, then the kernel of is
1. A matrix.
2. A number (possibly non-zero).
3. Zero.
4. Undefined.
5. A matrix.
6. A subspace of .
7. A subspace of .
• CORRECT.
17. If is a matrix, then the row-reduced echelon form of is
1. A matrix.
• CORRECT.
2. A number (possibly non-zero).
3. Zero.
4. Undefined.
5. A matrix.
6. A subspace of .
7. A subspace of .
• CORRECT.