Answered: 5. Let V = M2×2, {: ]=v W1(R) = E V :…

5. Let V = M2×2, {: ]=v W1(R) = E V : a, b, c ER W,(R) = {|% ev : a, beR E V : a, bER then prove that W1 and W2 are subspaces of V, and find the dimension of W1, W2, and W1NW2 respectively.

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

5. Let V = M2×2,
{: :
E V : a, b, ce R
a
Wi(R) =
{[". :]
W2(R) =
E V : a, bE R
-a
then prove that W1 and W2 are subspaces of V, and find the dimension
of W1, W2, and WinW2 respectively.

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