S4 = {4 € M2x2 (R)| det (A) = 1} Remembering that M2x2 ( R) is the set of 2x2 matrices with entries in R, check the correct options:Warning: when you mark a wrong one it cancels the right one.Choose one or more: a. None of the sets S1, S2, S3 e S4 is vector subspace. b. Only S1 e S2 are vector subspaces. c. Sz it is not a subspace of R“, but if we change the condition of y = x´ for y = 2x, we get a subspace. d. Są it is not a subspace of M22 ( R), but if we change the det condition (A) =1 to det (A) = 0, we get a subspace.

S4 = {4 € M2x2 (R)| det (A) = 1} Remembering that M2x2 ( R) is the set of 2x2 matrices with entries in R, check the correct options:Warning: when you mark a wrong one it cancels the right one.Choose one or more: a. None of the sets S1, S2, S3 e S4 is vector subspace. b. Only S1 e S2 are vector subspaces. c. Sz it is not a subspace of R“, but if we change the condition of y = x´ for y = 2x, we get a subspace. d. Są it is not a subspace of M22 ( R), but if we change the det condition (A) =1 to det (A) = 0, we get a subspace.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

About the sets,

S1 = {(x, y, z) ER|3x – 5y+3z = 10}
S2 = {(x, y, z)|y > 2}
S3 = {(x, y) E R² |y = x² }

S4 = {A € M2x2 (R)| det (A) = 1}
Remembering that M22 (R) is the set of 2x2 matrices with
entries in R, check the correct options:Warning: when you mark
a wrong one it cancels the right one.Choose one or more:
a. None of the sets S1, S2, S3 e S4 is vector subspace.
b. Only S1 e S2 are vector subspaces.
c. Sz it is not a subspace of R“, but if we change the condition
2
of y
= x for y = 2x, we get a subspace.
d. Są it is not a subspace of M22 (R), but if we change the det
condition (A) =1 to det (A) = 0, we get a subspace.

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