20. T(x1,X2,x3, X4) = 2x1 + 3x3 – 4x4 (T : R* → R) %3D

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 19EQ
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In Exercises 17-20, show that T is a linear transformation by
finding a matrix that implements the mapping. Note that x1, X2, . ..
are not vectors but are entries in vectors.
17. T(x1,X2, X3, X4) = (0, x1 + X2, X2 + x3, X3 + X4)
%3D
18. T(x1,x2) = (2x2 – 3.x1, X1 – 4x2, 0, x2)
19. T(x1,X2,x3) = (x1 – 5x2 + 4x3, x2 – 6x3)
20. T(x1,X2, X3, x4) = 2x1 + 3x3 – 4x4
(T : R+ → R)
Transcribed Image Text:In Exercises 17-20, show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, X2, . .. are not vectors but are entries in vectors. 17. T(x1,X2, X3, X4) = (0, x1 + X2, X2 + x3, X3 + X4) %3D 18. T(x1,x2) = (2x2 – 3.x1, X1 – 4x2, 0, x2) 19. T(x1,X2,x3) = (x1 – 5x2 + 4x3, x2 – 6x3) 20. T(x1,X2, X3, x4) = 2x1 + 3x3 – 4x4 (T : R+ → R)
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