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jeff1evesque
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I've chosen another problem in the book, but am not clear of how to begin. Could someone help me.
Instructions:
Determine whether the given set of invertible nxn matrices with real number entries is a subgroup of [tex]GL(n, R).[/tex]
Problem:
The nxn matrices with determinant -1.
Definition:
If a subset H of a group G is closed under the binary operation of G and if H with the induced operation from G is itself a group, then H is a subgroup of G.
Questions:
In the instructions (above), what does the notation [tex]GL(n, R)[/tex] denote? I looked for similar notations in the respective section of the book, but couldn't find anything.
What is meant by the following: ...and if H with the induced operation from G is itself a group..."?
Is the binary operation defined as the equation for taking the determinant?
To test whether we have a subgroup, do we just use the group axioms: closure, associativity, identity element, inverse element? I'm guessing if the group axioms pass (for our given subset), then the set is a subgroup?
Thanks,JL
Instructions:
Determine whether the given set of invertible nxn matrices with real number entries is a subgroup of [tex]GL(n, R).[/tex]
Problem:
The nxn matrices with determinant -1.
Definition:
If a subset H of a group G is closed under the binary operation of G and if H with the induced operation from G is itself a group, then H is a subgroup of G.
Questions:
In the instructions (above), what does the notation [tex]GL(n, R)[/tex] denote? I looked for similar notations in the respective section of the book, but couldn't find anything.
What is meant by the following: ...and if H with the induced operation from G is itself a group..."?
Is the binary operation defined as the equation for taking the determinant?
To test whether we have a subgroup, do we just use the group axioms: closure, associativity, identity element, inverse element? I'm guessing if the group axioms pass (for our given subset), then the set is a subgroup?
Thanks,JL