Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
D,E only please
![be XW
Ansagdada
tollen
1. Which of the following sets constitute a vector space? The answer must
be in one of the two forms:
V is a vector space because it is closed under addition and multiplication
by scalars (this means that mentally you checked that it is closed under
these operations and they satisfy the eight required properties)
or
V is not a vector space because ... (give a reason and support this reason
with an example).
bacola
(a) The set M₁of all 2x2 lower-triangular matrices:
a
= {all [8]}
(b) The set M₂ of all 6x1, 3x2, 2x3, and 1×6 matrices.
(c) The set V₁ of all vectors in the right-hand side of the xy-plane:sqa
strate your answer with a picture.
A
a1
are an 20}. Illu
a2
(d) The set V₂ all of all vectors on the line y = x in the xy-plane:
sola
do
V₂ =
= {all [d]}. Illustrate your answer with a picture. If the answer is
.
negative, also give a second reason (with an example).
M₁
V₁
(ap
"
=
sob wan JadW
(e) The set V3 of all vectors of the length one in a plane:
x
Amo
85
where x² + y² = 1}. Illustrate your answer with a pic-
V3
ture. If the answer is negative, also give a second reason (with an example).
(f) The got Or of all fourth-order polynomials with
ba bezols ad
po
sto](https://content.bartleby.com/qna-images/question/801d34df-dcab-45aa-85e0-2349cce424a4/dfe85f54-9551-45a8-9199-d1899acfedc5/khixohb_processed.jpeg)
Transcribed Image Text:be XW
Ansagdada
tollen
1. Which of the following sets constitute a vector space? The answer must
be in one of the two forms:
V is a vector space because it is closed under addition and multiplication
by scalars (this means that mentally you checked that it is closed under
these operations and they satisfy the eight required properties)
or
V is not a vector space because ... (give a reason and support this reason
with an example).
bacola
(a) The set M₁of all 2x2 lower-triangular matrices:
a
= {all [8]}
(b) The set M₂ of all 6x1, 3x2, 2x3, and 1×6 matrices.
(c) The set V₁ of all vectors in the right-hand side of the xy-plane:sqa
strate your answer with a picture.
A
a1
are an 20}. Illu
a2
(d) The set V₂ all of all vectors on the line y = x in the xy-plane:
sola
do
V₂ =
= {all [d]}. Illustrate your answer with a picture. If the answer is
.
negative, also give a second reason (with an example).
M₁
V₁
(ap
"
=
sob wan JadW
(e) The set V3 of all vectors of the length one in a plane:
x
Amo
85
where x² + y² = 1}. Illustrate your answer with a pic-
V3
ture. If the answer is negative, also give a second reason (with an example).
(f) The got Or of all fourth-order polynomials with
ba bezols ad
po
sto
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