Mastering Determinants: A Scientist's Approach to Solving Equations

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Homework Statement



PZn1tG3.png


Homework Equations





The Attempt at a Solution



XdrDSIB.png
 
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Turion said:

Homework Statement



PZn1tG3.png


Homework Equations





The Attempt at a Solution



XdrDSIB.png

What is your question?
 
If you are trying to evaluate the determinant, there is an arithmetic mistake in calculating the first 2x2 minor, specifically in calculating a12*a21.
 
Thanks. I make so many dumb mistakes. :(
 
Turion said:
Thanks. I make so many dumb mistakes. :(

You mean like not stating the question?
 

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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