8. Each of the following sets are not a subspace of the specified vector space. For each set, give a reason why it is not a subspace. (a) Let M2x2 be the vector space of all 2 x 2 real matrices. Se = {A € M2x2 | det(A) # 0} in the vector space M2x2. (b) Let M2x2 be the vector space of all 2 x 2 real matrices. S6 = {A € M2x2 | det(A) = 0} in the vector space M2x2. (c) Let C[-1, 1] be the vector space of all real continuous functions defined on the interval [a, b). Sg = {f(x) € C[-2, 2] | f(-1)ƒ(1) = 0} in the vector space C[-2, 2].

8. Each of the following sets are not a subspace of the specified vector space. For each set, give a reason why it is not a subspace. (a) Let M2x2 be the vector space of all 2 x 2 real matrices. Se = {A € M2x2 | det(A) # 0} in the vector space M2x2. (b) Let M2x2 be the vector space of all 2 x 2 real matrices. S6 = {A € M2x2 | det(A) = 0} in the vector space M2x2. (c) Let C[-1, 1] be the vector space of all real continuous functions defined on the interval [a, b). Sg = {f(x) € C[-2, 2] | f(-1)ƒ(1) = 0} in the vector space C[-2, 2].

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...

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