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Select all the true statements. Let T: R" → R", then T (0) = 0. T(7) = (0) V € Vis not a linear transformation. O Linear transformations are never defined by matrices.

Select all the true statements. Let T: R" → R", then T (0) = 0. T(7) = (0) V € Vis not a linear transformation. O Linear transformations are never defined by matrices.

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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Select all the true statements. L Let T: R™ → R", then T(0) ỏ. = ✓T(x) ~T(x) = (0) VE Vis not a linear transformation. Linear transformations are never defined by matrices. T: R"R" be a linear transformation induced by matrix A. T can have an inverse transformation if A is singular. Let T: RR" then T( – v) – T(v). A linear transformation T: R → Rm has the property that T(kč + pý) = kT(x) + pT(ÿ) for vectors and y in R" and scalars k and p. ✔ Let T: R" → Rm be a linear transformation then I is one to one if and only if T = = 0.
Transcribed Image Text:Select all the true statements. L Let T: R™ → R", then T(0) ỏ. = ✓T(x) ~T(x) = (0) VE Vis not a linear transformation. Linear transformations are never defined by matrices. T: R"R" be a linear transformation induced by matrix A. T can have an inverse transformation if A is singular. Let T: RR" then T( – v) – T(v). A linear transformation T: R → Rm has the property that T(kč + pý) = kT(x) + pT(ÿ) for vectors and y in R" and scalars k and p. ✔ Let T: R" → Rm be a linear transformation then I is one to one if and only if T = = 0.
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