Linear Algebra – 4.6 Rank of a Matrix and Systems of Linear Equations

The the basis of the row, column and null spaces of A. Then find the solutions to nonhomogeneous systems of equations.

Video Chapters:
0:00 Introduction
0:08 Row and Column Vectors
1:30 Theorems about Row Space
3:01 Find Row and Column Spaces (Method 1) and Rank
7:53 Find Col A – Method 2
11:13 Find Row and Column Spaces and Rank – Practice
14:18 The Null Space of a Matrix
16:58 Find the Null Space – Example 1
21:30 Find the Null Space – Example 2
25:15 Check for Understanding
27:42 Putting it All Together
36:27 Solutions to Nonhomogeneous Systems
39:55 Summary of Equivalent Statements
40:34 Up Next

Textbook: Elementary Linear Algebra 8e, Ron Larson

Slide Decks: https://bellevueuniversity-my.sharepoint.com/:f:/g/personal/kbrehm_bellevue_edu/IgDVnTt2BohsRLsMfseN5FijAXYDd49YlIkHeq5cfmCxG2g?e=ZwTt3c

Playlist: https://youtube.com/playlist?list=PLl-gb0E4MII1RjTV2GegmXFTJwTrek8OI&si=g3Xc3yHB5GkmxMF4