(a) Consider the real linear map T : R' - R', expressed as follows: X1 + 2x2 - x3 4x1 + 9x2 - x3 1 2 -1 49 -1 X1 X1 T i.e. TX2 %3D %3D X2 X2 2x1 +7x2 +7x3, X3 27 7 (i) Find a basis for the kernel of T. (ii) Find a basis for the image of T. (iii) Does the image of T include every vector in R'? Justity your answer. (You are not required to verify that your answers to (a)(i), (a)(i) are bases.)
(a) Consider the real linear map T : R' - R', expressed as follows: X1 + 2x2 - x3 4x1 + 9x2 - x3 1 2 -1 49 -1 X1 X1 T i.e. TX2 %3D %3D X2 X2 2x1 +7x2 +7x3, X3 27 7 (i) Find a basis for the kernel of T. (ii) Find a basis for the image of T. (iii) Does the image of T include every vector in R'? Justity your answer. (You are not required to verify that your answers to (a)(i), (a)(i) are bases.)
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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