Question

How do you find the rank collumn space and nullity of a matrix?

Answer 1

To find the rank of a matrix you row reduce. You will be left with rows with leading 1s

Answer 2

Count how many rows there are.

Answer 3

doesn't it have to do with the span of the linear combinations?

Answer 4

Let me be a little bit more clear. The dimension of the source space will be the number of columns in the matrix. So just subtract the rank from the number of columns and you will have your nullity.

Answer 5

As for nullity suppose you have the following transformation \(f:V\to W\).
\[\dim V = \text{rank}\ T + \text{nullity}\ T\]

Answer 6

thanks

Answer 7

http://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem