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W and V are linear spaces with dimension 2, the base of each of which is (e,, ez). If the linear conversion w is defined as follows: T(e, + e2) = 3e, + 9e, ,T(3e, + 2e2) = 7e, + 23e2 A) Find T (e - e2)and determine the emptiness and rank of T. B) Find the matrices T for the bases (e,, e2).

W and V are linear spaces with dimension 2, the base of each of which is (e,, ez). If the linear conversion w is defined as follows: T(e, + e2) = 3e, + 9e, ,T(3e, + 2e2) = 7e, + 23e2 A) Find T (e - e2)and determine the emptiness and rank of T. B) Find the matrices T for the bases (e,, e2).

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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W and V are linear spaces with dimension 2, the base of each of which is (e,, ez). If the linear conversion w is defined as follows: T(e, + e2) = 3e, + 9e2 ,T(3e, + 2e2) = 7e, + 23e2 A) Find T (e, - e2)and determine the emptiness and rank of T. B) Find the matrices T for the bases (e,, e2).
Transcribed Image Text:W and V are linear spaces with dimension 2, the base of each of which is (e,, ez). If the linear conversion w is defined as follows: T(e, + e2) = 3e, + 9e2 ,T(3e, + 2e2) = 7e, + 23e2 A) Find T (e, - e2)and determine the emptiness and rank of T. B) Find the matrices T for the bases (e,, e2).
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