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.