Question

Can some one help me , I dont understand what it means when the columns of a 4 X 4 matrix do not span R^4

Answer 1

* does not

Answer 2

One of the columns is a linear combination of the other three.

Answer 3

1) Your first column spans some of R^4
2) Adding the second column, we span a little more of R^4.
3) Adding a third column, we span even more of R^4.
4) Since the 4th one is a linear combination of the other 3, we get no new information and we span no more of R^4.

Answer 4

THank you tkhunny

Answer 5

Just to clarify... It isn't necessarily just one. It may be that three are multiples of the first, or that the second two are multiples of the first two.