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

generals336

Answered question

2021-02-09

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?

Answer & Explanation

Talisha

Talisha

Skilled2021-02-10Added 93 answers

Step 1 
The given set is { [a11b]|a,bK} 
It is understood that the identity element must be present in every subspace.
Step 2 
Note that the identity matrix [1001] does not belongs to { [a11b]|a,bK} Thus, NO is the response. the collection of all form 2 x 2 matrices { [a11b]|a,bK} is not a subspace of all matrices of size 2 x 2.

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-14Added 2605 answers

Answer is given below (on video)

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