ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 04 Jun 2017 13:47:41 +0200How to decide if T maps R^5 onto R^5https://ask.sagemath.org/question/37765/how-to-decide-if-t-maps-r5-onto-r5/ 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?
ThanksFri, 02 Jun 2017 18:24:59 +0200https://ask.sagemath.org/question/37765/how-to-decide-if-t-maps-r5-onto-r5/Comment by tmonteil for <p>Hi all,</p>
<p>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?</p>
<p>Thanks</p>
https://ask.sagemath.org/question/37765/how-to-decide-if-t-maps-r5-onto-r5/?comment=37773#post-id-37773This is not a question about Sage, but about the mathematics you learnt. Which notion is useful to know whether a linear map in onto ?Sat, 03 Jun 2017 00:45:31 +0200https://ask.sagemath.org/question/37765/how-to-decide-if-t-maps-r5-onto-r5/?comment=37773#post-id-37773Comment by dan_fulea for <p>Hi all,</p>
<p>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?</p>
<p>Thanks</p>
https://ask.sagemath.org/question/37765/how-to-decide-if-t-maps-r5-onto-r5/?comment=37787#post-id-37787I 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?
sage: A = matrix( QQ, [ [ 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] ] )
sage: A.det()
0
sage: A.rank()
4
sage: ImA = A.image()
sage: ImA.dimension()
4
sage: KerA = A.kernel()
sage: KerA.dimension()
1Sun, 04 Jun 2017 13:47:41 +0200https://ask.sagemath.org/question/37765/how-to-decide-if-t-maps-r5-onto-r5/?comment=37787#post-id-37787