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## Homework Statement

Consider the following ket: |ψ

_{i}> = c

_{1}|e

_{1}> + c

_{2}|e

_{2}>, where c

_{i}are some complex coefficients. Find the column-vector representation of |ψ

_{i}> in the |e

_{i}> basis. Find the row-vector representation of <ψ| in the <e

_{i}| basis.

## Homework Equations

|ψ

_{i}> = c

_{1}|e

_{1}> + c

_{2}|e

_{2}>

## The Attempt at a Solution

Well I'm not sure what to do so I tried to start off by solving c

_{1}and c

_{2}. To do this I multiplied |ψ

_{i}> = c

_{1}|e

_{1}> + c

_{2}|e

_{2}> by <e

_{1}| to get that c

_{1}= <e

_{1}|ψ> . Multiplying the same equation by <e

_{2}| gives c

_{2}= <e

_{2}|ψ>

So I wrote |ψ> = <e

_{1}|ψ|e

_{1}> + <e

_{2}|ψ|e

_{2}>

Now I'm not sure what to do

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