Comment. Elementary matrix quiz
Comment. This quiz is designed to test basic concepts concerning matrices and vectors.
Shuffle Questions.
Shuffle Answers.
Question. Let A be an 3 x 4 matrix, and let B be a 4 x 3 matrix. Which of the four operations A x B, B x A, A + B, A - B make sense?
Correct Answer. A x B and B x A make sense.
Answer. A+B and A-B make sense.
Answer. None of the operations make sense.
Answer. A x B makes sense.
Answer. All of the operations make sense.
Answer. A+B makes sense.
Answer. B x A makes sense.
Question. Let A be an 3 x 4 matrix, and let B be a 4 x 5 matrix. Which of the four operations A x B, B x A, A + B, A - B make sense?
Answer. A x B and B x A make sense.
Answer. A+B and A-B make sense.
Answer. None of the operations make sense.
Correct Answer. A x B makes sense.
Answer. All of the operations make sense.
Answer. A+B makes sense.
Answer. B x A makes sense.
Question. Let A be an 3 x 4 matrix, and let B be a 3 x 4 matrix. Which of the four operations A x B, B x A, A + B, A - B make sense?
Answer. A x B and B x A make sense.
Correct Answer. A+B and A-B make sense.
Answer. None of the operations make sense.
Answer. A x B makes sense.
Answer. All of the operations make sense.
Answer. A+B makes sense.
Answer. B x A makes sense.
Question. Let A be an 3 x 3 matrix, and let B be a 3 x 3 matrix. Which of the four operations A x B, B x A, A + B, A - B make sense?
Answer. A x B and B x A make sense.
Answer. A+B and A-B make sense.
Answer. None of the operations make sense.
Answer. A x B makes sense.
Correct Answer. All of the operations make sense.
Answer. A+B makes sense.
Answer. B x A makes sense.
Question. If one multiplies a row vector by a column vector, one gets
Answer. Nothing; this operation cannot be defined in general.
Correct Answer. A number, if the two vectors have the same length, and nothing (undefined) otherwise.
Answer. A number.
Answer. A matrix.
Answer. A row vector.
Answer. A column vector.
Answer. An L-shaped vector.
Question. If one adds a row vector to a column vector, one gets
Correct Answer. Nothing; this operation cannot be defined in general.
Answer. A number, if the two vectors have the same length, and nothing (undefined) otherwise.
Answer. A number.
Answer. A matrix.
Answer. A row vector.
Answer. A column vector.
Answer. An L-shaped vector.
Question. If one multiplies a matrix with a column vector, one gets
Answer. Nothing; this operation cannot be defined in general.
Correct Answer. A column vector, if the number of columns of the matrix matches the number of rows of the vector.
Answer. A column vector, if the number of rows of the matrix matches the number of columns of the vector.
Answer. A column vector, if the number of rows of the matrix matches the number of rows of the vector.
Answer. A matrix.
Answer. A row vector.
Answer. A number.
Question. If one multiplies a column vector with a row vector, one gets
Answer. Nothing; this operation cannot be defined in general.
Answer. A column vector, if both vectors have the same length.
Answer. A row vector, if both vectors have the same length.
Answer. A column vector, in all cases.
Correct Answer. A matrix.
Answer. A row vector, in all cases.
Answer. A number.
Question. If one multiplies a column vector with a matrix, one gets
Correct Answer. Nothing; this operation cannot be defined in general.
Answer. A column vector, if the number of columns of the matrix matches the number of rows of the vector.
Answer. A column vector, if the number of rows of the matrix matches the number of columns of the vector.
Answer. A column vector, if the number of rows of the matrix matches the number of rows of the vector.
Answer. A matrix.
Answer. A row vector.
Answer. A number.
Question. Let A be a matrix. Under what conditions will A x A will make sense?
Correct Answer. A must be a square matrix.
Answer. A must have at least as many rows as columns.
Answer. A must have at least as many columns as rows.
Answer. A must be a row vector.
Answer. A must be a column vector.
Answer. A x A makes sense for any matrix A.
Answer. A must be in reduced row-echelon form.
Question. If A is a 3 x 5 matrix, then the determinant of A is
Answer. A 3 x 5 matrix.
Answer. A number (possibly non-zero).
Answer. Zero.
Correct Answer. Undefined.
Answer. A 5 x 3 matrix.
Answer. A subspace of R^3.
Answer. A subspace of R^5.
Question. If A is a 3 x 5 matrix, then the rank of A is
Answer. A 3 x 5 matrix.
Correct Answer. A number (possibly non-zero).
Answer. Zero.
Answer. Undefined.
Answer. A 5 x 3 matrix.
Answer. A subspace of R^3.
Answer. A subspace of R^5.
Question. If A is a 3 x 5 matrix, then the transpose of A is
Answer. A 3 x 5 matrix.
Answer. A number (possibly non-zero).
Answer. Zero.
Answer. Undefined.
Correct Answer. A 5 x 3 matrix.
Answer. A subspace of R^3.
Answer. A subspace of R^5.
Question. If A is a 3 x 5 matrix, then the inverse of A is
Answer. A 3 x 5 matrix.
Answer. A number (possibly non-zero).
Answer. Zero.
Correct Answer. Undefined.
Comment. Only square matrices can be invertible.
Answer. A 5 x 3 matrix.
Answer. A subspace of R^3.
Answer. A subspace of R^5.
Question. If A is a 3 x 5 matrix, then the image of A is
Answer. A 3 x 5 matrix.
Answer. A number (possibly non-zero).
Answer. Zero.
Answer. Undefined.
Answer. A 5 x 3 matrix.
Correct Answer. A subspace of R^3.
Answer. A subspace of R^5.
Question. If A is a 3 x 5 matrix, then the kernel of A is
Answer. A 3 x 5 matrix.
Answer. A number (possibly non-zero).
Answer. Zero.
Answer. Undefined.
Answer. A 5 x 3 matrix.
Answer. A subspace of R^3.
Correct Answer. A subspace of R^5.
Question. If A is a 3 x 5 matrix, then the row-reduced echelon form of A is
Correct Answer. A 3 x 5 matrix.
Answer. A number (possibly non-zero).
Answer. Zero.
Answer. Undefined.
Answer. A 5 x 3 matrix.
Answer. A subspace of R^3.
Correct Answer. A subspace of R^5.