15.R. Let f be a linear function of R2 into R3 which sends the elements €1 = (1, 0), ez = (0, 1) of R' into the vectors f(e1) = (2, 1, 0), f(e:) = (1,0, -1) of R. Give the matrix representation of f. What vectors in R³ are the images under f of the elements %3D (2, 0), (1, 1), (1, 3)? 15.S. If f denotes the linear function of Exercise 15.R, show that not every vector in R3 is the image under f of a vector in R'.
15.R. Let f be a linear function of R2 into R3 which sends the elements €1 = (1, 0), ez = (0, 1) of R' into the vectors f(e1) = (2, 1, 0), f(e:) = (1,0, -1) of R. Give the matrix representation of f. What vectors in R³ are the images under f of the elements %3D (2, 0), (1, 1), (1, 3)? 15.S. If f denotes the linear function of Exercise 15.R, show that not every vector in R3 is the image under f of a vector in R'.
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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15.-
Transcribed Image Text:15.R. Let f be a linear function of R? into R3 which sends the elements
(1, 0), e2
€1 = = (0, 1) of R' into the vectors f(e1) = (2, 1, 0), f(e:) =
of R3. Give the matrix representation of f. What vectors in R3 are the images
under f of the elements
(1, 0, -1)
(2, 0), (1, 1), (1, 3)?
15.S. If f denotes the linear function of Exercise 15.R, show that not every
vector in R3 is the image under f of a vector in R'.
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