How many of the following subsets of the space M2(R) are subspaces of this space?a){A E M2 (R): det(A) # 0} b){A € M,(R): A" = A} c) {A € M2 (R): A" = -A}a12a2.%3D%3D29 -a11d) {A € M2(R):rankA= 1} e) {la a:Eij=141}=0}O A) 5O B) 4C) 3O D) 2O E) 1

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How many of the following subsets of the space M2(R) are subspaces of this space? a){A € M2(R): det(A) # 0} b) {A € M2(R): A" = A} c) {A € M2(R): A™ = -A} a11 a12) d) {A € M2(R):rankA= 1} e) {[ ]:E=1 ª; j = 0}

How many of the following subsets of the space M2(R) are subspaces of this space? a){A € M2(R): det(A) # 0} b) {A € M2(R): A" = A} c) {A € M2(R): A™ = -A} a11 a12) d) {A € M2(R):rankA= 1} e) {[ ]:E=1 ª; j = 0}

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 59CR

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

How many of the following subsets of the space M2(R) are subspaces of this space?
a){A E M2 (R): det(A) # 0} b){A € M,(R): A" = A} c) {A € M2 (R): A" = -A}
a12
a2.
%3D
%3D
29 -
a11
d) {A € M2(R):rankA= 1} e) {la a:Eij=141}=0}
O A) 5
O B) 4
C) 3
O D) 2
O E) 1

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