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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.

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.

Advanced Engineering Mathematics
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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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.
Transcribed Image Text: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.
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