SOLUTION: Determine which of the following are subspaces of M22. (i) All matrices a b where a+b+c+d=0 c d (ii) All 2×2 matrices A such that det (A)=0 (iii) All

Question 1182856: Determine which of the following are subspaces of M22.
(i) All matrices a b where a+b+c+d=0
c d
(ii) All 2×2 matrices A such that det (A)=0
(iii) All the matrices of the form a b
0 c
Answer by ikleyn(53765) (Show Source): You can put this solution on YOUR website!
.


If you know the definition of a sub-space (which I assume), then you easily will come to the following answers:


(i)    YES


(ii)   NO  (because det(A) = 0 and det(B) = 0 do not imply det(A+B) = 0)


(iii)  YES

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