Presentation is loading. Please wait.

Presentation is loading. Please wait.

Subspaces, Basis, Dimension, Rank

Similar presentations


Presentation on theme: "Subspaces, Basis, Dimension, Rank"— Presentation transcript:

1 Subspaces, Basis, Dimension, Rank

2 Subspace

3 Theorem

4 Example Let V be the set of all vectors in with length at most 1. Is V a subspace?

5 Example Is V a subspace?

6 Basis

7 Dimension

8 Null Space

9 Nullity

10 Rank Theorem

11 Example

12 Example

13 Definition of Row and Column Space

14 Theorem

15 Theorem

16 Example Find the linear relations between the columns.

17 Row and Column Rank

18 Theorem

19 Theorem

20 Example Find the rank and the linear relations between the rows.

21 Fundamental Theorem of Invertible Matrices

22 Examples

23


Download ppt "Subspaces, Basis, Dimension, Rank"

Similar presentations


Ads by Google