Mathematics: Applications and Interpretation · Topic 1: Number and algebra

AHL1.14 — Matrices

Mathematics: Applications and Interpretation · SL / HL · syllabus-mapped notes

1. AIAHL1.14.1

   Matrices: definition and algebra

   Order $m\times n$; equality, addition, subtraction, scalar multiplication.

2. AIAHL1.14.2

   Matrix multiplication and its properties

   Row-by-column product; associative and distributive but not commutative; $I$ and $0$.

3. AIAHL1.14.3

   Determinant and inverse

   $\det A=ad-bc$ and $A^{-1}$ for $2\times2$ by hand, larger with technology.

4. AIAHL1.14.4

   Solving linear systems with matrices

   Writing $A\mathbf{x}=\mathbf{b}$ and solving via $\mathbf{x}=A^{-1}\mathbf{b}$; coding messages.