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Quiz: Elementary matrices
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last edited
by Issa Rice 5 years, 3 months ago
This quiz is designed to test basic concepts concerning matrices and vectors.
Discuss this quiz
(Key: correct, incorrect, partially correct.)
- Let be an matrix, and let be a matrix. Which of the four operations , , , make sense?
- and make sense.
- and make sense.
- None of the operations make sense.
- makes sense.
- All of the operations make sense.
- makes sense.
- makes sense.
- Let be an matrix, and let be a matrix. Which of the four operations , , , make sense?
- and make sense.
- and make sense.
- None of the operations make sense.
- makes sense.
- All of the operations make sense.
- makes sense.
- makes sense.
- Let be an matrix, and let B be a matrix. Which of the four operations , , , make sense?
- and make sense.
- and make sense.
- None of the operations make sense.
- makes sense.
- All of the operations make sense.
- makes sense.
- makes sense.
- Let be an matrix, and let B be a matrix. Which of the four operations , , A + B, A - B make sense?
- and make sense.
- and make sense.
- None of the operations make sense.
- makes sense.
- All of the operations make sense.
- makes sense.
- makes sense.
- If one multiplies a row vector by a column vector, one gets
- Nothing; this operation cannot be defined in general.
- A number, if the two vectors have the same length, and nothing (undefined) otherwise.
- A number.
- A matrix.
- A row vector.
- A column vector.
- An L-shaped vector.
- If one adds a row vector to a column vector, one gets
- Nothing; this operation cannot be defined in general.
- A number, if the two vectors have the same length, and nothing (undefined) otherwise.
- A number.
- A matrix.
- A row vector.
- A column vector.
- An L-shaped vector.
- If one multiplies a matrix with a column vector, one gets
- Nothing; this operation cannot be defined in general.
- A column vector, if the number of columns of the matrix matches the number of rows of the vector.
- A column vector, if the number of rows of the matrix matches the number of columns of the vector.
- A column vector, if the number of rows of the matrix matches the number of rows of the vector.
- A matrix.
- A row vector.
- A number.
- If one multiplies a column vector with a row vector, one gets
- Nothing; this operation cannot be defined in general.
- A column vector, if both vectors have the same length.
- A row vector, if both vectors have the same length.
- A column vector, in all cases.
- A matrix.
- A row vector, in all cases.
- A number.
- If one multiplies a column vector with a matrix, one gets
- Nothing; this operation cannot be defined in general.
- A column vector, if the number of columns of the matrix matches the number of rows of the vector.
- A column vector, if the number of rows of the matrix matches the number of columns of the vector.
- A column vector, if the number of rows of the matrix matches the number of rows of the vector.
- A matrix.
- A row vector.
- A number.
- Let be a matrix. Under what conditions will will make sense?
- must be a square matrix.
- must have at least as many rows as columns.
- must have at least as many columns as rows.
- must be a row vector.
- must be a column vector.
- makes sense for any matrix .
- must be in reduced row-echelon form.
- If is a matrix, then the determinant of is
- A matrix.
- number (possibly non-zero).
- Zero.
- Undefined.
- A matrix.
- A subspace of .
- A subspace of .
- If is a matrix, then the rank of is
- A matrix.
- A number (possibly non-zero).
- Zero.
- Undefined.
- A matrix.
- A subspace of .
- A subspace of .
- If is a matrix, then the transpose of is
- A matrix.
- A number (possibly non-zero).
- Zero.
- Undefined.
- A matrix.
- A subspace of .
- A subspace of .
- If is a matrix, then the inverse of is
- A matrix.
- A number (possibly non-zero).
- Zero.
- Undefined.
- CORRECT. Only square matrices can be invertible.
- A matrix.
- A subspace of .
- A subspace of .
- If is a matrix, then the image of is
- A matrix.
- A number (possibly non-zero).
- Zero.
- Undefined.
- A matrix.
- A subspace of .
- A subspace of .
- If is a matrix, then the kernel of is
- A matrix.
- A number (possibly non-zero).
- Zero.
- Undefined.
- A matrix.
- A subspace of .
- A subspace of .
- If is a matrix, then the row-reduced echelon form of is
- A matrix.
- A number (possibly non-zero).
- Zero.
- Undefined.
- A matrix.
- A subspace of .
- A subspace of .
Score:
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Quiz: Elementary matrices
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