Equation point from a matrix

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Homework Statement


Good evening everyone,, I have the following problem:
attachment.php?attachmentid=24867&stc=1&d=1270403123.png



The Attempt at a Solution



disregarding the digit ,, he's giving me P(x) and want P(A) but A is a matrix ,, should I get the determinant of A then apply it in the equation ?? or it has some idea I need to know ??
 

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You know how to multiply matrices

You know how to add matrices

I dare say maybe you can just plug in A directly and get an answer. This is pretty common, giving a polynomial where you think the input is supposed to be a number, but then you plug in matrices instead to see what you get
 
And since P(A) involves matrices, not numbers, be sure to use I in place of 1 in your formula for P(A).
 
aha, got it ... Really it's very easy ,, I feel stupid :shy:

Thanks very much guys
 
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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