4.Let H be the set of 2 x 2 whose trace is equal to zero. That is-{:a11a12Н —E M2(R) | a11 + a22 =A21 a22Prove that H is a subspace of M2(R).

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Answered: 4. Let H be the set of 2 × 2 whose…

4. Let H be the set of 2 × 2 whose trace is equal to zero. That is [a11 a12 Н- E M2(R) | a11 + a22 = 0 a22 Prove that H is a subspace of M2(R).

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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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

4.
Let H be the set of 2 x 2 whose trace is equal to zero. That is
-{:
a11
a12
Н —
E M2(R) | a11 + a22 =
A21 a22
Prove that H is a subspace of M2(R).

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