BitWithBite
Mathematics Worksheet
🔢 Determinants
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After this worksheet you can
Compute a 2×2 determinant.Compute a 3×3 determinant by cofactor expansion.Relate a zero determinant to invertibility.Interpret the determinant as an area scale factor.📚 Quick Recap
The determinant condenses an entire square matrix into a single number that reveals whether the matrix is invertible and how it scales area or volume.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1det[[5,3],[2,4]] = ?
2det[[7,1],[1,7]] = ?
3If a matrix has determinant 0, it is:
4A 3×3 determinant is computed by:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5det[[a,b],[c,d]] = .
6det[[5,3],[2,4]] = .
7Find the determinant of [[5,3],[2,4]].
8Find the determinant of [[7,1],[1,7]].
9Find the determinant of [[1,0,2],[3,1,0],[0,2,1]] by cofactor expansion.
🚀 Section C · Challenge ● CHALLENGE 5
10Is the matrix [[6,2],[3,1]] (det = 0) invertible?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-A 2-A 3-B 4-A | 5 ad − bc 6 14 7 = 14 8 = 48 9 = 1+12 = 13 | 10 = No, its determinant is 0