MA 305 Lecture 18 Transparencies

Tuesday, April 4, 2000


Slide 0

Parameterized solution of linear system. (Lecture 3, Slide 7).
(Audio part 1, 6:00)

Lecture 18, slide 0


Slide 1

Solution of linear system is not vector space; it is translation of null space.
(Audio part 1, 7:30 and 29:00)

Lecture 18, slide 1


Slide 2

Augmented matrix and solution from Lecture 3, Slide 7.
(Audio part 1, 15:00)

Lecture 18, slide 2


Slide 3

Solution of linear system is translation of null space continued.
(Audio part 1, 30:30)

Lecture 18, slide 3


Slide 4

Example of column space.
(Audio part 1, 36:00)

Lecture 18, slide 4


Slide 5

Example of column space continued.
Example of rank.
(Audio part 2, 0:00)

Lecture 18, slide 5


Slide 6

Example of row space.
Dimensions of row and column spaces are equal.
(Audio part 2, 4:30)

Lecture 18, slide 6


Slide 7

Conditions on solvability of linear system.
(Audio part 2, 23:00, 28:00, and 30:00)

Lecture 18, slide 7


Slide 8

Proof of conditions on solvability of linear system.
(Audio part 2, 27:00 and 28:30)

Lecture 18, slide 8