How can I determine if the matrix A spans ?

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- Mar 21st 2011, 01:11 PMposix_memalignDoes the matrix span R^4?
How can I determine if the matrix A spans ?

- Mar 21st 2011, 01:14 PMAckbeet
- Mar 21st 2011, 01:46 PMposix_memalign
- Mar 21st 2011, 06:21 PMAckbeet
Right-ho. Then the way I would go about it is this: let the columns of be denoted They are column vectors in Let

be an arbitrary vector in We want to know if there is a set of scalars, such that

right? Now, this equation that I've just written down can be translated into a system of equations for the unknown constants Your goal is to determine the rank of the coefficient matrix for that system. If the rank is 4, then you've got yourself a spanning set with those 's. Otherwise, if the rank is less than 4, you don't. Make sense? Where would you go next? - Mar 21st 2011, 06:58 PMposix_memalign
- Mar 21st 2011, 07:01 PMAckbeet
- Mar 22nd 2011, 10:44 AMposix_memalign
- Mar 22nd 2011, 10:57 AMAckbeet
Hmm. WolframAlpha disagrees with you. Maybe you should re-check your work?

- Mar 23rd 2011, 12:40 PMposix_memalign
- Mar 23rd 2011, 12:41 PMAckbeet
That's correct, it does not.