For Exercises 2 through 6, prove that T is a linear transformation, and find bases for...

Transcribed Image Text:

For Exercises 2 through 6, prove that T is a linear transformation, and find bases for both N(T) and R(T). Then compute the nullity and rank of T, and verify the dimension theorem. Finally, use the appropriate theorems in this section to determine whether T is one-to-one or onto. 2. T: R3 - R? defined by T(a1, a2, a3) = (a1 - a2, 2a3). %3! 3. T: R2 - R3 defined by T(a1, a2) = (a1 + a2, 0, 2a1 - a2). %3D For Exercises 2 through 6, prove that T is a linear transformation, and find bases for both N(T) and R(T). Then compute the nullity and rank of T, and verify the dimension theorem. Finally, use the appropriate theorems in this section to determine whether T is one-to-one or onto. 2. T: R3 - R? defined by T(a1, a2, a3) = (a1 - a2, 2a3). %3! 3. T: R2 - R3 defined by T(a1, a2) = (a1 + a2, 0, 2a1 - a2). %3D

Answer rating: 100% (QA)

TR3 R for NIT taiandas O 109 Mullity T dim NIt 1 ... View the full answer