1. Vectors, Linear Combinations and Linear Independence

2. Vectors in Rn
Vectors in Rn:

3. Vectors in Rn
Vector operations:
Equality:
Addition:

4. Vectors in Rn
Multiplication by scalar:
Magnitude:

5. Vectors in Rn
Dot (scalar) product:

6. Vectors in Rn
Example:

7. Vectors in Rn
Properties:

8. Linear Combinations
Definition:

9. Linear Combinations
Example 1:

10. Linear Combinations
Example 2:

11. Linear Dependence and Independence
Definition:

12. Linear Dependence and Independence
Example :

13. Linear Dependence and Independence
Note:

14. Linear Dependence and Independence
Note:

15. Linear Dependence and Independence
Example: