1. Let V = M2,2(Q), the vector space of 2 x 2 matrices with rational coefficients. Decide which of the following subsets of V is a vector subspace of V. In each case, either give a proof that it is a subspace or demonstrate an axiom that is not satisfied. {(: ) - {(: ') -{{: :) : (a - e)0 – 4) = 0}. a : ас — 1 W1 : 2a – b = c+d W3 WĄ а,

1. Let V = M2,2(Q), the vector space of 2 x 2 matrices with rational coefficients. Decide which of the following subsets of V is a vector subspace of V. In each case, either give a proof that it is a subspace or demonstrate an axiom that is not satisfied. {(: ) - {(: ') -{{: :) : (a - e)0 – 4) = 0}. a : ас — 1 W1 : 2a – b = c+d W3 WĄ а,

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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Concept explainers

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

1. Let V = M2,2(Q), the vector space of 2 x 2 matrices with rational coefficients. Decide which of the
following subsets of V is a vector subspace of V. In each case, either give a proof that it is a subspace
or demonstrate an axiom that is not satisfied.
- {(: ')
-{{: :) : (a - e)0 – 4) = 0}.
a
W1
: 2a – b = c+d
: ас — 1
a
W3
а,
WĄ
|
c d

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