EXM.1.AHL.TZ0.27

pestleMathematicsAIHLPaper 1EXM· ahl-1-14-introduction-to-matricessource ↗

Let A, B and C be non-singular 2×2 matrices, I the 2×2 identity matrix and k a scalar. The following statements are incorrect. For each statement, write down the correct version of the right hand side.

(A + B)² = A² + 2AB + B²

[2]

(A – kI)³ = A³ – 3kA² + 3k²A – k³

[2]

CA = B C = $\frac{B}{A}$

[2]

Markscheme / solution

(A + B)² = A² + AB + BA + B² A2

Note: Award A1 in parts (a) to (c) if error is correctly identified, but not corrected.

[2 marks]

(A – kI)³ = A³ – 3kA² + 3k²A – k³I A2

Note: Award A1 in parts (a) to (c) if error is correctly identified, but not corrected.

[2 marks]

CA = B ⇒ C = BA^–1 A2

Note: Award A1 in parts (a) to (c) if error is correctly identified, but not corrected.

[2 marks]

Examiners’ report

[N/A]