2. Prove or disprove that the following are vector spaces 3 -7 22 (a) Let M = The set {x R3 | Mx = 0} -1 0 1 (b) Let M = (³ 3 -7 22 -1 7 22) The set {x = R³ | Mx = (*) 4 (c) The set all polynomials with even powers (d) The set F = {f: RR | f is not continuous at 0} with usual function addition and scalar multiplication

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Prove or disprove that the following are vector spaces
3
-7
22
(a) Let M
=
The set {x R3 | Mx = 0}
-1
0
1
(b) Let M
=
(³
3 -7 22
-1
7 22)
The set {x = R³ | Mx =
(*)
4
(c) The set all polynomials with even powers
(d) The set F = {f: RR | f is not continuous at 0} with usual function addition and scalar
multiplication
Transcribed Image Text:2. Prove or disprove that the following are vector spaces 3 -7 22 (a) Let M = The set {x R3 | Mx = 0} -1 0 1 (b) Let M = (³ 3 -7 22 -1 7 22) The set {x = R³ | Mx = (*) 4 (c) The set all polynomials with even powers (d) The set F = {f: RR | f is not continuous at 0} with usual function addition and scalar multiplication
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