Solving the Formula Without Matrix Inverses: A,B,C & b

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If A,B and C are nxn matrice, with B and C nonsingular, and b is an n-vector, how would you implement the formula



x = B-1(2A+I)(C-1+A)b, without computing any matrix inverse?



I made it Bx=(2A+1)C-1(I+CA)b, but don't know how to pull out the C-1 from the middle in order to take the equation without matrices inverse,sigh.. but I don't know if I approached it right because I don't even get the question.

Please help me!
Thank you very much :frown:
 
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The furthest I could come was by working out the parentheses:

CBx = (2CAC-1+2CA2+I+A)b

I hope someone else can get some answer...
 


Euphz said:
If A,B and C are nxn matrice, with B and C nonsingular, and b is an n-vector, how would you implement the formula



x = B-1(2A+I)(C-1+A)b, without computing any matrix inverse?



I made it Bx=(2A+1)C-1(I+CA)b, but don't know how to pull out the C-1 from the middle in order to take the equation without matrices inverse,sigh.. but I don't know if I approached it right because I don't even get the question.

Please help me!
Thank you very much :frown:
What do you mean "implement the formula"? Is the goal to evaluate the right hand side of the original equation to get x?
 

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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