Assume that T is a linear transformation,T: R3 →· R?, T(e,) = ( 1, 3), T(e2) = ( 4,–7 ), and T (e;) = (-5, 4)where e,, e2, ez are the columns of the 3 x 3 identity matrix. Determine if the specified lineartransformation isа)one-to-oneb)(Justify each answer)onto

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Answered: Assume that T is a linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let T : R" → R" be a linear transformation with standard matrix A. Which of the following is not a characterization of the statement “T is surjective"? OA. RREF(A) has a pivot in every row О в. Im T = R" Oc. The columns of A span R" OD. RREF(A) has a pivot in every column
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Assume that T is a linear transformation, T: R3 → · R², T(e,) = ( 1, 3 ), T(e2) = ( 4,– 7 ), and T (e;) = (-5, 4) where e,, e2, ez are the columns of the 3 x 3 identity matrix. Determine if the specified linear transformation is а) one-to-one b) onto