1. Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector subspace of all 2 x 2 matrices?

generals336 2021-02-09 Answered
1. Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector subspace of all 2 x 2 matrices?
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Talisha
Answered 2021-02-10 Author has 93 answers
Step 1
The given set is {[a11b]|a,bK}
It is known that any subspace should contain the identity element.
Step 2
Note that the identity matrix [1001] does not belongs to {[a11b]|a,bK} Thus, the answer is NO. the set of all 2 x 2 matrices of the form {[a11b]|a,bK} is not a subspace of all 2 x 2 matrices.
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Jeffrey Jordon
Answered 2022-01-14 Author has 2064 answers

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