Question: 4. The matrix 2 3 5 1 1 0 2 2 4 is singular. Let T be a linear transformation whose standard matrix is A.

4. The matrix 2 3 5 1 1 0 2 2 4 is singular. Let T be a linear transformation whose standard matrix is A. Answer the following questions. (a) What are the domain and codomain of T? Explain in a sentence or two how this relates to the size of A. (b) Express the range of T as a span of as few vectors as possible. (c) Explain in a sentence or two why T is not onto. (d) Explain in a sentence or two why the fact that T is not onto means A must be singular. (e) Compute T 1 1 1 and T 0 0 0 . (f) Explain in a sentence or two why T is not one-to-one. (g) Explain in a sentence or two why the fact that T is not one-to-one means A must be singular

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