Vocabulary
row, column, entry, order, square, zero, diagonal, identity I, singular.
🎯 Final Checkpoint Readiness Map
Before attempting the checkpoint, make sure you can explain each idea—not only perform the calculation.
Operations
Add and subtract matching entries. Apply a scalar to every entry. Multiply using row × column.
Determinant and inverse
For 2 × 2 matrices, calculate ad − bc. An inverse exists only when the determinant is non-zero.
Equations
Recognise AX = B and solve X = A⁻¹B while preserving multiplication order.
Identity test
AI = IA = A
AA⁻¹ = I
AA⁻¹ = I
Final checking
Check signs, order, answer dimensions and substitution into original equations.
Mastery Question: Could you teach a classmate why the identity matrix is written I and why it behaves like 1?
Final Checkpoint
- Define a matrix and state the order of 123456.
- Find 2A−B for A=3124, B=15−23.
- State whether (2×3)(3×1) is possible and give product order.
- Multiply 21−13 by 425−2.
- Find det7321.
- Find k if k428 is singular.
- Find inverse of 4131.
- Solve AX=B for A=2112, B=87.
- Solve 2x+3y=13 and x+y=5.
✅ Check Your Work
Show answers and working
- A matrix is a rectangular array; order 3×2.
- 5−365.
- Yes; 2×1.
- 13211−8.
- 1.
- k=1.
- 1−1−34.
- X=32.
- x=2, y=3.
✅ Final Interactive Checkpoint
📘 Remember
Key idea
Strong matrix work combines correct conditions, careful arithmetic and clear notation.
⚠️ Common Mistakes
Rushing order checks is one of the most common causes of avoidable errors.
⭐ Exam Tips
Use any remaining time to verify dimensions, signs, determinant values and multiplication order.
🌍 Did You Know?
The word matrix comes from a Latin word meaning womb or source—something from which other things develop.