1. Transformations

2. matrix and column vector product
𝑎 𝑐 𝑏 𝑑 𝑥 𝑦 =𝑥 𝑎 𝑏 +𝑦 𝑐 𝑑 = 𝑎𝑥+𝑦𝑐 𝑏𝑥+𝑦𝑑

3. 2D translation

4. 2D scaling

5. 2D reflection

7. “Young [wo]man, in mathematics you don't understand things
“Young [wo]man, in mathematics you don't understand things. You just get used to them.” John von Neumann

8. homogenous coordinates

9. 2D translation
using algebraic notation: using matrices:

10. 2D scaling
using algebraic notation: using matrices:

11. 2D reflection about x-axis about y-axis
𝑥 ′ 𝑦 ′ 1 = − 𝑥 𝑦 1

12. 2D shearing
using algebraic notation: using matrices:

13. 2D rotation
using algebraic notation: using matrices: