Week 5 - Section 4.5 and Section 4.6 - June 21 - June 25

Textbook Readings	Video	Lecture Notes
Section 4.5 The Dimension of a Vector Space (pp. 227 - 232)	Section 4.5 Video	Section 4.5 Lecture notes
Section 4.6 Rank (pp. 232 - 241)	Section 4.6 Video	Section 4.6 Lecture notes

Section 4.5 The Dimension of a Vector Space	Section 4.6 Rank
Definition of the dimension of a Vector Space; computing a basis. Find dimension of a subspaces by computing a basis. Dimension of a Rn and Pn Discuss the Basis Theorem. Dimension of column and null space of A and how they relate to the number of columns of A, pivots and free variables.	Definition of row space of A. Finding a basis for row space of A and relationship with rref of A. Learn that the dimension of the column space and row space are the same Discuss the definition of Rank and relationship with dimension of the column space and row space. The Rank Theorem, relationship rank with dimension of null space and number columns of A. Introduce the term nullity - the dimension of null space. In video, not in notes. Add statements to Invertible Matrix Theorem from section 2.3.
Download section 4.5 lecture notes and watch the video. Practice the textbook problems (Not Graded) 1, 3, 5, 7, 11, 13, 17, 21, 22 Worksheet for Section 4.5. Use the Assignments tool within Brightspace. Due: 11:55pm June 23 Use the Discussion tool within Brightspace to ask questions.	Download section 4.6 lecture notes and watch video. Practice the textbook problems (Not Graded) 1, 3, 5, 7, 11, 25, 26, 31 Worksheet for Section 4.6. Use the Assignments tool within Brightspace. Due: 11:55pm June 23 Use the Discussion tool within Brightspace to ask questions.
WeBWorK for Sections 4.5 and 4.6 Due: 11:55pm June 25