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Question

Suppose A is a matrix such that A2=A and (I+A)10=I+kA, find k.

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Solution

Given A2=A
(I+A)10=I+kA
10C0I+10C1A+10C2A2+10C3A3+....10C10A10=I+kA
I+(10+45+120+210+252+210+120+45+10+1)A=I+kA
k=1023

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