Thread: Linear algebra question

If anyone could explain how the following is done, it would be greatly appreciated.

Give an example of the following. If no example exists, explain why.

- A set of vectors in M sub 3,4 which are linearly independent but do not span M sub 3, 4

Originally Posted by faure72

If anyone could explain how the following is done, it would be greatly appreciated.

Give an example of the following. If no example exists, explain why.

- A set of vectors in M sub 3,4 which are linearly independent but do not span M sub 3, 4

Assuming that M_{3,4} denotes the set of all 3x4 matrices (over R?)

[1,0,0,0]
[0,0,0,0]
[0,0,0.0]

and

[0,1,0,0]
[1,0,0,0]
[0,0,0,0]

are linearly independent and do not span M_{3,4} and so are the elements
of a set with the desired property.

RonL

Originally Posted by CaptainBlack

Assuming that M_{3,4} denotes the set of all 3x4 matrices (over R?)

[1,0,0,0]
[0,0,0,0]

and

[0,1,0,0]
[1,0,0,0]

are linearly independent and do not span M_{3,4} and so are the elements
of a set with the desired property.

RonL

would not those matrices need a third row? since they have to be elements of M_{3,4}?

Originally Posted by Jhevon

would not those matrices need a third row? since they have to be elements of M_{3,4}?

Opps.. yes of course (goes back and modifies post so no one will ever
know CB made a mistake )

RonL