MA 305 Lecture 16 Transparencies

Thursday, March 23, 2000

Slide 1

Null space.
Proof null space is subspace.
(Audio part 1, 8:00)

Lecture 16, slide 1

Slide 2

Example of null space: implicit definition of plane.
(Audio part 1, 14:00 and 26:00)

Lecture 16, slide 2

Slide 3

Spanning set for null space.
Explicit definition of null space; parametric solution.
(Audio part 1, 21:00, 28:00, and 34:30; and part 2, 25:30)

Lecture 16, slide 3

Slide 4

Checking for membership in plane.
(Audio part 1, 39:30)

Lecture 16, slide 4

Slide 5

Finding implicit definition of plane.
(Audio part 1, 35:00)

Lecture 16, slide 5

Slide 6

Finding implicit definition of plane continued.
Null space examples: two-fold and hyperplane.
(Audio part 1, 38:30)

Lecture 16, slide 6

Slide 7

Line in hyperspace.
Two-fold example continued.
(Audio part 2, 8:00)

Lecture 16, slide 7

Slide 8

Big Definition: Basis of vector space.
(Audio part 2, 13:30)

Lecture 16, slide 8

Slide 9

Example that basis is not unique.
(Audio part 2, 17:30)

Lecture 16, slide 9

Slide 10

Uniqueness of linear combination of basis vectors.
(Audio part 2, 21:30)

Lecture 16, slide 10