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March 2nd, 2009, 01:44 PM  #1 
Newbie Joined: Mar 2009 Posts: 3 Thanks: 0  Linear Algebra.Linear Transformations.Help!!
The problem is: "Let S a linear transformation from R^3 to R^2 and T a linear transformation from R^2 to R^3. Show that TS is not invertible." Have anyone can help me to the above problem. Thanks anyone in advance.

March 2nd, 2009, 07:28 PM  #2 
Member Joined: Jan 2009 Posts: 72 Thanks: 0  Re: Linear Algebra.Linear Transformations.Help!!
There is an infinity of vectors (in fact a 1dimensional manifold) in R3 that are preimages of any vector in the range of TS. Thus, TS cannot be 11 (i.e., it's not injective) and therefore has no left inverse. Since an inverse is necessarily a left inverse, there can be no inverse.


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algebralinear, linear, transformationshelp 
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