Answer to Question #40302 in Linear Algebra for deepu singh

Question #40302

Let M2(R) be the vector space of all 2*2 matrices over R . Prove that M2(R)=S+T , where S={A belongs to M2(R)|aii=0 , i=1,2} and T={B belongs to M2(R)|bij=0 , i does not equal to the j } are subspaces of M2(R).

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