One of the following is Not trueA) W = {(a, b, c) : a < b} is a subspace of RB) W = {(a, b, c) : b = 2e + a} is a subspace of RC) W = {A € Mnn : tr(A) = 0} is a subspace of Mn%3D%3DD) W = {A € Mnn: A is lower} is a subspace of Mnn%3D7n7n

By using the subspace test. Answer : option (A)

One of the following is Not true A) W = {(a, b, c) : a < b} is a subspace of R %3D B) W = {(a, b, c) : b = 2c + a} is a subspace of R %3D C) W = {A e Mnn : tr(A) = 0} is a subspace of Mnn %3D %3D D) W = {A € Mnn : A is lower} is a subspace of Mn %3D 7172

One of the following is Not true A) W = {(a, b, c) : a < b} is a subspace of R %3D B) W = {(a, b, c) : b = 2c + a} is a subspace of R %3D C) W = {A e Mnn : tr(A) = 0} is a subspace of Mnn %3D %3D D) W = {A € Mnn : A is lower} is a subspace of Mn %3D 7172

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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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

One of the following is Not true
A) W = {(a, b, c) : a < b} is a subspace of R
B) W = {(a, b, c) : b = 2e + a} is a subspace of R
C) W = {A € Mnn : tr(A) = 0} is a subspace of Mn
%3D
%3D
D) W = {A € Mnn: A is lower} is a subspace of Mnn
%3D
7n7n

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