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->> The linear operator T: R³ R³ is defined by T(x1, x2, 3) = (x₁+3x2+2x3, x2 - I3, I3) Which of the following is correct. (a) T is one to one but the standard matrix for T-1 does not exist. 1-3 2 (b) T is one to one and its standard matrix for T-1 is 0 -1 00 1 1 (c) T is one to one and its standard matrix for T-1 is 0 0 (d) T is not one to one (e) None of these -3 1 0 -5 1 1

->> The linear operator T: R³ R³ is defined by T(x1, x2, 3) = (x₁+3x2+2x3, x2 - I3, I3) Which of the following is correct. (a) T is one to one but the standard matrix for T-1 does not exist. 1-3 2 (b) T is one to one and its standard matrix for T-1 is 0 -1 00 1 1 (c) T is one to one and its standard matrix for T-1 is 0 0 (d) T is not one to one (e) None of these -3 1 0 -5 1 1

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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->> The linear operator T: R³ R³ is defined by T(x1, x2, 3) = (x1+3x2+2x3, x2 - I3, I3) Which of the following is correct. (a) T is one to one but the standard matrix for T-1 does not exist. 13 2 0 1 0 0 (b) T is one to one and its standard matrix for T-¹ is 1 (c) T is one to one and its standard matrix for T-¹ is 0 0 (d) T is not one to one (e) None of these 1 -3 -5 1 1 0 1
Transcribed Image Text:->> The linear operator T: R³ R³ is defined by T(x1, x2, 3) = (x1+3x2+2x3, x2 - I3, I3) Which of the following is correct. (a) T is one to one but the standard matrix for T-1 does not exist. 13 2 0 1 0 0 (b) T is one to one and its standard matrix for T-¹ is 1 (c) T is one to one and its standard matrix for T-¹ is 0 0 (d) T is not one to one (e) None of these 1 -3 -5 1 1 0 1
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