Please give a clear and complete solution. Linear algebra and differential equations Consider the set U ={A = M₂ (R) |AT = A}. Given that M₂ (R) is the vector space of 2x2 matrices with real number entries, show that U is also a vectorspace. (Hint: there is a quick way and a long way to do this)• Find a basis for U and show that your basis is, indeed, a basis..• Conclude the problem by finding the dimension of U.

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Answered: Consider the set U = {A = M₂ (R) |AT =…

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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Please give a clear and complete solution. Linear algebra and differential equations

Consider the set U =
{A = M₂ (R) |AT = A}
. Given that M₂ (R) is the vector space of 2x2 matrices with real number entries, show that U is also a vector
space. (Hint: there is a quick way and a long way to do this)
• Find a basis for U and show that your basis is, indeed, a basis.
.
• Conclude the problem by finding the dimension of U.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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