# How to decide if T maps R^5 onto R^5

Hi all,

New to SageMath, for a homework problem I have to use SageMath to solve a problem and this problem is, "Decide if T maps R^5 onto R^5." This is the matrix ([[9,13,5,6,-1],[14,15,-7,-6,4],[-8,-9,12,-5,-9],[-5,-6,-8,9,8],[13,14,15,2,11]]). How do I go about proving this in SageMath?

Thanks

This is not a question about Sage, but about the mathematics you learnt. Which notion is useful to know whether a linear map in onto ?

I decided on a similar site to give the code in similar situations, thus offering a change to understand math supported by computer soft and computer examples.

(I will work over rationals, well $-\otimes_{\mathbb Q}\mathbb R$ is exact.)

Which of the following computations does (not) answer the problem?