MA 305 Lecture 17 Transparencies

Tuesday, March 28, 2000

Slide 1

Infinite dimensional vector space of polynomials.
(Audio part 1, 0:00)

Lecture 17, slide 1

Slide 2

Cardinality comparisons among infinite sets.
(Audio part 1, 9:00 and 18:30)

Lecture 17, slide 2

Slide 3

Dimension of Vector Space.
(Audio part 1, 22:00 and 28:30)

Lecture 17, slide 3

Slide 4

Linear independence and spanning sets for finite vector spaces.
(Audio part 1, 28:00 and 30:30)

Lecture 17, slide 4

Slide 5

Examples of proving linear independence and dependence.
(Audio part 1, 33:30, and part 2, 0:30)

Lecture 17, slide 5

Slide 6

Creating basis for vector space.
(Audio part 1, 40:30, and part 2, 5:00)

Lecture 17, slide 6

Slide 7

Picture of extending set of linearly independent vectors to basis for vector space.
(Audio part 2, 6:30 and 14:00)

Lecture 17, slide 7

Slide 8

Example of extending set of linearly independent vectors to basis for vector space.
(Audio part 2, 9:30)

Lecture 17, slide 8

Slide 9

Row- and Column-Spaces of matrix.
(Audio part 2, 18:00)

Lecture 17, slide 9

Slide 10

Rank of matrix.
Solvability theorem.
(Audio part 2, 23:00)

Lecture 17, slide 10