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Let V be a vector space with basis B and let 7(x) = [x] denote the coordinate mapping. Select all items below that apply. A. If T(x) = T(y), then x = y. ✔B. For any b in R", there is an xin V such that T(x) = b. ☐C.T' is onto but might not be one-to-one. ✔D. T(0) may or may not be 0, it depends on V and B. E. T is one-to-one and onto. F. I might be neither onto nor one-to-one. ✓G. T' is one-to-one but might not be onto. ⒸH. There may be vectors x y such that T(x) = T(y). LT(0) = 0

Let V be a vector space with basis B and let 7(x) = [x] denote the coordinate mapping. Select all items below that apply. A. If T(x) = T(y), then x = y. ✔B. For any b in R", there is an xin V such that T(x) = b. ☐C.T' is onto but might not be one-to-one. ✔D. T(0) may or may not be 0, it depends on V and B. E. T is one-to-one and onto. F. I might be neither onto nor one-to-one. ✓G. T' is one-to-one but might not be onto. ⒸH. There may be vectors x y such that T(x) = T(y). LT(0) = 0

Advanced Engineering Mathematics
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 V be a vector space with basis B and let 7(x) = [x] denote the coordinate mapping. Select all items below that apply. A. If T(x) = T(y), then x = y. ✔B. For any b in R", there is an xin V such that T(x) = b. ☐C.T' is onto but might not be one-to-one. ✔D. T(0) may or may not be 0, it depends on V and B. E. T is one-to-one and onto. F. I might be neither onto nor one-to-one. ✓G. I' is one-to-one but might not be onto. H. There may be vectors x y such that T(x) = T(y). LT(0) = 0
Transcribed Image Text:Let V be a vector space with basis B and let 7(x) = [x] denote the coordinate mapping. Select all items below that apply. A. If T(x) = T(y), then x = y. ✔B. For any b in R", there is an xin V such that T(x) = b. ☐C.T' is onto but might not be one-to-one. ✔D. T(0) may or may not be 0, it depends on V and B. E. T is one-to-one and onto. F. I might be neither onto nor one-to-one. ✓G. I' is one-to-one but might not be onto. H. There may be vectors x y such that T(x) = T(y). LT(0) = 0
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