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March 2nd, 2009, 01:44 PM   #1
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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.
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March 2nd, 2009, 07:28 PM   #2
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Re: Linear Algebra.Linear Transformations.Help!!

There is an infinity of vectors (in fact a 1-dimensional manifold) in R3 that are preimages of any vector in the range of TS. Thus, TS cannot be 1-1 (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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