2. Let M2x2 (R) be the set of all 2 x 2 matrices (with real number entries). That is a b {[%] | a, b, c, d in R} C d M2x2(R) = { is a vector space. Let H = The set M2x2 (R) with the zero matrix 0 = a {[%] C d 00 -[88 0 0 (a) Give a nonzero element of H. 7 with the usual addition and scalar multiplication | a, c, d in R} be a subset of M2×2 (R). (b) Give an element of M2x2 (R) which is not in H. (c) Is H a subspace of M2x2 (R)? Justify your answer.
2. Let M2x2 (R) be the set of all 2 x 2 matrices (with real number entries). That is a b {[%] | a, b, c, d in R} C d M2x2(R) = { is a vector space. Let H = The set M2x2 (R) with the zero matrix 0 = a {[%] C d 00 -[88 0 0 (a) Give a nonzero element of H. 7 with the usual addition and scalar multiplication | a, c, d in R} be a subset of M2×2 (R). (b) Give an element of M2x2 (R) which is not in H. (c) Is H a subspace of M2x2 (R)? Justify your answer.
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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Question
![2. Let M2x2 (R) be the set of all 2 x 2 matrices (with real number entries). That is
a
b
[29]
C
d
M2x2 (R)
is a vector space. Let H =
The set M2x2 (R) with the zero matrix 0
=
=
a 0
с d
0
0
0 0
nR}
| a, b, c, d in
with the usual addition and scalar multiplication
(a) Give a nonzero element of H.
(b) Give an element of M2x2 (R) which is not in H.
(c) Is H a subspace of M2x2 (R)? Justify your answer.
| a, c, d in R be a subset of M2x2 (R).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e97a7-c018-42d1-8011-94e3d67c6fc2%2F4d67646b-dff0-4749-a275-c03a4ffa2d99%2Fktvugwb_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let M2x2 (R) be the set of all 2 x 2 matrices (with real number entries). That is
a
b
[29]
C
d
M2x2 (R)
is a vector space. Let H =
The set M2x2 (R) with the zero matrix 0
=
=
a 0
с d
0
0
0 0
nR}
| a, b, c, d in
with the usual addition and scalar multiplication
(a) Give a nonzero element of H.
(b) Give an element of M2x2 (R) which is not in H.
(c) Is H a subspace of M2x2 (R)? Justify your answer.
| a, c, d in R be a subset of M2x2 (R).
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