27. a. Show that the line through vectors p and q in R" may be written in the parametric form x = (1 – t)p+fq. (Refer to the figure with Exercises 21 and 22 in Section 1.5.) b. The line segment from p to q is the set of points of the form (1 t)p+tq for 0 ≤ t ≤ 1 (as shown in the figure below). Show that a linear transformation T maps this line segment onto a line segment or onto a single point. (t = 1)q (1-t)p+tq - X (t = 0) p
27. a. Show that the line through vectors p and q in R" may be written in the parametric form x = (1 – t)p+fq. (Refer to the figure with Exercises 21 and 22 in Section 1.5.) b. The line segment from p to q is the set of points of the form (1 t)p+tq for 0 ≤ t ≤ 1 (as shown in the figure below). Show that a linear transformation T maps this line segment onto a line segment or onto a single point. (t = 1)q (1-t)p+tq - X (t = 0) p
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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Answer 27 please
Transcribed Image Text:5 ep
and
let
into
for
stify
fined
must be true about T(u) and T(v) in order for the image of
the plane P to be a plane?
27. a. Show that the line through vectors p and q in R" may be
written in the parametric form x
=
(1-t)p+fq. (Refer
to the figure with Exercises 21 and 22 in Section 1.5.)
b. The line segment from p to q is the set of points of the
form (1 t)p+tq for 0 ≤ t ≤ 1 (as shown in the figure
below). Show that a linear transformation T maps this
line segment onto a line segment or onto a single point.
(t = 1)q
(1-t)p+tq
X
(t = 0) p
28. Let u and v be vectors in R". It can be shown that the set P of
all points in the parallelogram determined by u and v has the
form au + bv, for 0 < a < 1,0 < b < 1. Let T: R" → Rm
Search
H
X
W
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