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
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(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
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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(53763) (Show Source):
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
