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Question

If A=[3141] and A10=[a11a12a21a22],then a11+a22=

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Solution

A=[3141]=[1001]+[2142] =I+BB2=[2142][2142]=[0000]Now, A10=(I+B)10=I+10C1B+10C2B2+10C3B3+...+10C10B10=I+10B=[1001]+10[2142]=[21104019]a11+a22=2119=2

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