Discrete Math Proof: Solving Homework Equations

Bashyboy
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Homework Statement


I attached the problem as a file.


Homework Equations





The Attempt at a Solution


I get stuck on how to properly represent the summation. How does k find it's way as one of the sub-scripts?
 

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Your post makes no sense and there is no attachment.
 
I am so sorry, I'll fix that.
 
Okay, you have BTAT. Now, what is (AB)T?
 
So,

AB = \sum_k a_{ki}b_{jk}

(AB)^t = \sum_k a_{ki} b_{jk} = \sum_k b_{jk} a_{ki} = B^tA^t

Does that look correct?
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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