Linear algebra: determinants (proof)

yoda05378
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hi, i seem to have some trouble proving:

Suppose M = [A B:O C], where A is a kxk matrix, C is a pxp matrix, and O is a zero matrix. Show that det(M) = det(A)det(C).


my attempt at a proof:

det(M) = det(A)det(C)

det[A B:O C] = det(A)det(C)

AC - OB = det(A)det(C)

AC = det(A)det(C) <-- doesn't make sense!

please point out where my logic failed.
 
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nevermind. i figured out where i went wrong (i treated the matrices as if they were scalar, stupid me). thanks for all the help :sarcasm:
 

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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