Suppose that T: R3 R3 is a linear transformation and = T 223 123 1. Determine...

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Suppose that T: R3 R3 is a linear transformation and = T 223 123 1. Determine T 2 3 (Note: you can do part 2 first and deduce this from it, if you want.) 2. Determine T 3. Find a matrix A such that T(X) = AX for all X R. 4. Find a basis for ker(T). 5. Find a basis for range(T). Suppose that T: R3 R3 is a linear transformation and = T 223 123 1. Determine T 2 3 (Note: you can do part 2 first and deduce this from it, if you want.) 2. Determine T 3. Find a matrix A such that T(X) = AX for all X R. 4. Find a basis for ker(T). 5. Find a basis for range(T).