Let ß and y be the standard ordered bases for R" and R", respectively. For the following transformations T: R* → R", compute [T]}. (а) Т: R? — R3 defined by T(а,, а2) — (2а, — а,, За, + 4а,, а). (b) T: R3 (c) T: R3 (d) T: R3 T(а, а,, аз) — (2а, + aз, — а, + 4a, t 5аз, а, + a). (е) Т: R" > R" defined by T (ај, а2, .., а,) 3D (ај, ај, ...,a). (() T:R" — R" defined by T(aj, аz, ..., an) 3 (ал, а, - 13 .., аj). (g) T: R" - R? defined by T(а,, а, аз) — (2а, + За, — аза а, + ag). > R defined bу T(а;, а2, а,) — 2а, + a, — Заз- R3 defined by R defined by T(a1, a2,..., a,) = a1 + a„.

Let ß and y be the standard ordered bases for R" and R", respectively. For the following transformations T: R* → R", compute [T]}. (а) Т: R? — R3 defined by T(а,, а2) — (2а, — а,, За, + 4а,, а). (b) T: R3 (c) T: R3 (d) T: R3 T(а, а,, аз) — (2а, + aз, — а, + 4a, t 5аз, а, + a). (е) Т: R" > R" defined by T (ај, а2, .., а,) 3D (ај, ај, ...,a). (() T:R" — R" defined by T(aj, аz, ..., an) 3 (ал, а, - 13 .., аj). (g) T: R" - R? defined by T(а,, а, аз) — (2а, + За, — аза а, + ag). > R defined bу T(а;, а2, а,) — 2а, + a, — Заз- R3 defined by R defined by T(a1, a2,..., a,) = a1 + a„.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...

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