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Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then...

Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then P = Q.

Expert Solution

Solution:

Let where is a vector space.

Call the mutual kernel and the mutual image .

Consider any and let

and .

Now,

, since for all .

So, .

where and .

, since and .

for every ,

Hence,

milcah answered 2 years ago

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