(d) 2910 Subspace of R², or explain why it is not a subspace of R2. For each of the following subsets of R2, either show that it is a (i) 2012910520291051 2910-(i) 20129105 291051 201291092051 S = {(0,0), (1, 1)1,01291051 79105 20129 2014 = {(x,x): r 20129102924) ER}. 051 201291051. 201291051 201291051 201291051 201291051 201291051 20129105 1201291051 20129105 701291051 201291051 1053 201291051 20129105 UR². 20129105 201291051 201291051201291051 201291051 201291051 20179105 1291051 201291051 701291051 201291051 20120105 701291051 20129105
(d) 2910 Subspace of R², or explain why it is not a subspace of R2. For each of the following subsets of R2, either show that it is a (i) 2012910520291051 2910-(i) 20129105 291051 201291092051 S = {(0,0), (1, 1)1,01291051 79105 20129 2014 = {(x,x): r 20129102924) ER}. 051 201291051. 201291051 201291051 201291051 201291051 201291051 20129105 1201291051 20129105 701291051 201291051 1053 201291051 20129105 UR². 20129105 201291051 201291051201291051 201291051 201291051 20179105 1291051 201291051 701291051 201291051 20120105 701291051 20129105
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
plz provide handwritten answer for question 4 part d
Transcribed Image Text:4. (a)
2012910 (a, a, a), v₂= (a.a+1, a +1) and v3 = (a, a, a + 1) linearly independent? 201291051
0 Let a be a real number. For which values of a are the vectors V₁
051 2012(b)
129105
051 201291
129105
by the vectors {V₁, V₂, V3} from part (a).
For each value of a, find the dimension of the subspace of R³ spanned 1051
(c)
20122105
(d)
R³?
For which values of a
20129173) form a basis f
For each of the following subsets of R2, either show that it is 391051
2012910 Subspace of R², or explain why it is not a subspace of R2.
9105
in part (a) does
{v₁,
051
1051
(i)
201291
20129105
051 20129105
for 1051
201051
20129102012910520291051,
1051
051 2012910 (ii)
051
20129 a
201291051 2012915 91051
{(0,0), (1, 1), 1291051,
0510127= {(r,r): r ERU{(y. 2y): y ER}.
2012
201291051
051 2012910 (1)
051 201291051
701291051
201291ER}U {(
20129105
201291051
201291051 201291051 201291051
201291051
201291051
201291051 201291051
1201291051 201291051
201291051
20129105 U= P²
201291051 201291051
771291051
701291051
201291051 201291051
701291051 201291051 201291051 201291051
701291051 201291051 201201051
701291051 201291051
701291051
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