QM - Spin operator conjugate question

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Homework Statement



Okay so I've got a question I really need answered first up! If I have a 2x1 matrix for Psi, is Psi* a 1x2 matrix with all the 'i's turned to '-i's?

Now onto the actual question - http://imgur.com/3ucb4" - part b only

Homework Equations



http://imgur.com/bcEm3"

(Sorry to URL everything)

The Attempt at a Solution



http://imgur.com/FW0dP"

What did I do wrong?
 
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Simply have the 2 x 2 matrix of Sx operate on the state v, then multiply your new 2 x 2 matrix with the conjugate of v.

And yes the conjugate of v is a transpose matrix with the i's all different.
 
Isn't that what I did? v is a 2x1 matrix. When I multiply Sx with v I'm left with a 2x1 matrix, not a 2x2.

Sx times v = v

v* times v = 2

Integral = infinity
 

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