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Quiz: Elementary matrices
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last edited
by Issa Rice 2 years 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:
.
Quiz: Elementary matrices
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