Comment. Determinant quiz
Comment. This quiz is designed to test basic properties of determinants.
Shuffle Questions.
Shuffle Answers.
Question. Let A be a 5x5 matrix with determinant 6. What is the determinant of A^{-1} (the inverse of A)?
Correct Answer. 1/6.
Answer. 6.
Answer. 0.
Answer. 30.
Answer. 25/6.
Answer. 1.
Answer. Insufficient information to solve the question.
Question. Let A be a 5x5 matrix with determinant 6, and let B be a 5x5 matrix with determinant 4. What is the determinant of AB?
Correct Answer. 24.
Answer. 10.
Answer. 0.
Answer. 1/6.
Answer. 1/4.
Answer. 1.
Answer. Insufficient information to solve the question.
Question. Let A be a 5x5 matrix with determinant 6, and let B be a 5x5 matrix with determinant 4. What is the determinant of A+B?
Answer. 24.
Answer. 10.
Answer. 0.
Answer. 1/6.
Answer. 1/4.
Answer. 1.
Correct Answer. Insufficient information to solve the question.
Question. Let A be a 4x4 matrix with determinant 3. What is the determinant of -A?
Correct Answer. 3.
Answer. -3.
Answer. 1/3.
Answer. 0.
Answer. 1.
Answer. -1.
Answer. Insufficient information to solve the question.
Question. Let A be a 4x4 matrix with determinant 3. What is the determinant of 2A?
Correct Answer. 48.
Answer. 6.
Answer. 3.
Answer. 24.
Answer. 12.
Answer. 196,608.
Answer. Insufficient information to solve the question.
Question. Let A be a 4x4 matrix with determinant 3. What is the determinant of A^t (the transpose of A)?
Correct Answer. 3.
Answer. 3^t.
Answer. 12.
Answer. 1/3.
Answer. 27.
Answer. 81.
Answer. Insufficient information to solve the question.
Question. Let A be a 4x4 matrix with determinant 3. Let B be the matrix formed by swapping the second and third rows of A. What is det(B)?
Correct Answer. -3.
Answer. 3.
Answer. 0.
Answer. 1/3.
Answer. 6.
Answer. 2.
Answer. Insufficient information to solve the question.
Question. Let A be a 4x4 matrix with determinant 3. Let B be the matrix formed by multiplying the fourth row of A by 2. What is det(B)?
Correct Answer. 6.
Answer. 3.
Answer. 3/2.
Answer. -48.
Answer. 48.
Answer. -6.
Answer. Insufficient information to solve the question.
Question. Let A be a 4x4 matrix with determinant 3. Let B be the matrix formed by dividing the fourth row of A by 2. What is det(B)?
Correct Answer. 3/2.
Answer. 3.
Answer. 6.
Answer. 3/16.
Answer. 3/4.
Answer. -3.
Answer. Insufficient information to solve the question.
Question. Let A be a 4x4 matrix with determinant 3. Let B be the matrix formed by adding two copies of the third row to the first. What is det(B)?
Correct Answer. 3.
Answer. 6.
Answer. 0.
Answer. -3.
Answer. -6.
Answer. 9.
Answer. Insufficient information to solve the question.
Question. Let A be a 4x4 matrix with determinant 3. Let B be the matrix formed by subtracting two copies of the third row from the first. What is det(B)?
Correct Answer. 3.
Answer. 6.
Answer. 0.
Answer. -3.
Answer. -6.
Answer. -9.
Answer. Insufficient information to solve the question.
Question. Let A be a 4x4 matrix. The relationship between determinant and invertibility is
Correct Answer. A is invertible if and only if its determinant is non-zero.
Answer. A is invertible if its determinant is non-zero, but not conversely.
Answer. The determinant of A is non-zero if and only if A is invertible, but not conversely.
Answer. A is invertible if and only if its determinant is zero.
Answer. A is invertible if its determinant is zero, but not conversely.
Answer. The determinant of A is zero if and only if A is invertible, but not conversely.
Answer. There is no connection between the two concepts.