Solve Matrix Questions: Reduce Rows in a Large Matrix

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Can someone help me understand how i can reduce rows in a large matrix? Not row reduction, just wen i can mark out rows that are redundant, i think if rows are multiples of each other you can mark out some of those rows?
 
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In what sense are you talking? A matrix is a representation of a linear map - you can't ignore any of it. If, however, you want to know its rank, then of course one can 'remove' duplicate rows, or rows that are multiples of one another. ('Remove' is wrong - replace by the row of all zeros would be a better idea.)
 
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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