Thread: finding matrix A

Let .
If for all ,
show that for any .

Originally Posted by deniselim17

Let .
If for all ,
show that for any .

One way is to write then select which gives you a=d and b=c, then select which gives you c=b=0. (Find AB and BA and set corresponding cells equal.)

Originally Posted by undefined

One way is to write then select which gives you a=d and b=c, then select which gives you c=b=0. (Find AB and BA and set corresponding cells equal.)

Since the question asked "for all B", I let .
But I can't continue.

Originally Posted by deniselim17

Since the question asked "for all B", I let .
But I can't continue.

If it's true for all B, it's certainly true for the particular B's I mentioned in my first post. Your approach might work but it seems a bit of a mess. Note that you're only asked to prove implication in one direction. Also note that the problem statement is a little imprecise in language, I would write "for some alpha" rather than "for any alpha". (Clearly it's an existential rather than universal statement, because the universal statement makes no sense.)

You might find this useful.

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