PRE CALCULUS Matrices and Vectors 1 — Questions and Answers
Question 1: What is the determinant of the matrix [[3, 1], [2, 4]]?
- 10 (Correct answer)
- 14
- 8
- 12
Correct answer: 10
The determinant of a 2×2 matrix [[a,b],[c,d]] is ad − bc = (3)(4) − (1)(2) = 10.
Question 2: Which operation is NOT defined for matrices A and B?
- A + B when dimensions differ (Correct answer)
- A × B when A is 2×3 and B is 3×2
- Scalar multiplication of A
- A − A
Correct answer: A + B when dimensions differ
Matrix addition requires both matrices to have identical dimensions.
Question 3: What is the result of multiplying a 2×3 matrix by a 3×4 matrix?
- 2×4 matrix (Correct answer)
- 3×3 matrix
- 2×3 matrix
- 6×4 matrix
Correct answer: 2×4 matrix
When multiplying an m×n matrix by an n×p matrix, the result is an m×p matrix, so 2×4.
Question 4: What is the identity matrix for 2×2 multiplication?
- [[1,0],[0,1]] (Correct answer)
- [[0,1],[1,0]]
- [[1,1],[1,1]]
- [[0,0],[0,0]]
Correct answer: [[1,0],[0,1]]
The identity matrix has 1s on the main diagonal and 0s elsewhere, leaving any matrix unchanged when multiplied.
Question 5: If vector u = ⟨3, −4⟩, what is |u|?
- 5 (Correct answer)
- 7
- 1
- √7
Correct answer: 5
The magnitude of vector ⟨a, b⟩ is √(a² + b²) = √(9 + 16) = √25 = 5.
Question 6: What does the dot product u · v = 0 indicate about vectors u and v?
- They are perpendicular (Correct answer)
- They are parallel
- They are equal
- They are unit vectors
Correct answer: They are perpendicular
A dot product of zero means the vectors are orthogonal (perpendicular) to each other.
PRE CALCULUS Matrices and Vectors 1
What is the determinant of the matrix [[3, 1], [2, 4]]?