peter_miller
peter_miller 3d ago • 0 views

Test yourself: Determinant properties with row/column operations questions.

Hey there, mathletes! 👋 Ready to boost your determinant skills? This study guide and quiz will help you master determinant properties with row/column operations. Let's dive in! 🧮
🧮 Mathematics
🪄

🚀 Can't Find Your Exact Topic?

Let our AI Worksheet Generator create custom study notes, online quizzes, and printable PDFs in seconds. 100% Free!

✨ Generate Custom Content

1 Answers

✅ Best Answer
User Avatar
Eco_Engineer Jan 6, 2026

📚 Quick Study Guide

  • 🔢 The determinant of a matrix changes sign when two rows (or columns) are interchanged.
  • ➕ Adding a multiple of one row (or column) to another row (or column) does not change the determinant.
  • ⚖️ If a row (or column) is multiplied by a scalar $k$, the determinant is multiplied by $k$.
  • 0️⃣ If a matrix has a row (or column) of zeros, its determinant is zero.
  • 🆔 The determinant of the identity matrix is 1.
  • ✖️ For a matrix $A$, if two rows or columns are identical, then $det(A) = 0$.
  • ✨ $det(AB) = det(A) \cdot det(B)$

Practice Quiz

  1. Question 1: If $A$ is a $3 \times 3$ matrix with $det(A) = 5$, and $B$ is obtained from $A$ by interchanging the first and third rows, then $det(B)$ is:
    1. 5
    2. -5
    3. 10
    4. 0
  2. Question 2: If $A$ is a $4 \times 4$ matrix with $det(A) = 2$, and $B$ is obtained from $A$ by multiplying the second row by 3, then $det(B)$ is:
    1. 2
    2. 6
    3. 8
    4. 1/2
  3. Question 3: If $A$ is a $3 \times 3$ matrix with $det(A) = -3$, and $B$ is obtained from $A$ by adding 2 times the first row to the third row, then $det(B)$ is:
    1. -3
    2. -6
    3. -1
    4. 0
  4. Question 4: If $A$ is a $2 \times 2$ matrix with $det(A) = 4$, and $B$ is obtained from $A$ by multiplying $A$ by 2 (i.e., $B = 2A$), then $det(B)$ is:
    1. 4
    2. 8
    3. 16
    4. 2
  5. Question 5: If $A$ is a $3 \times 3$ matrix with a row of zeros, then $det(A)$ is:
    1. 1
    2. -1
    3. 0
    4. Cannot be determined
  6. Question 6: If $A$ and $B$ are $2 \times 2$ matrices with $det(A) = 2$ and $det(B) = 3$, then $det(AB)$ is:
    1. 5
    2. 6
    3. 1
    4. 0
  7. Question 7: If $A$ is a $3 \times 3$ matrix, and $B$ is obtained from $A$ by swapping the first and second columns and then multiplying the third row by 4, and given that $det(A) = 1$, then $det(B)$ is:
    1. 1
    2. 4
    3. -4
    4. -1
Click to see Answers
  1. B
  2. B
  3. A
  4. C
  5. C
  6. B
  7. C

Join the discussion

Please log in to post your answer.

Log In

Earn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀