Projecting to the range of a matrix

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Homework Statement



Let U = span({(1, 2, 1)t, (1, 0, 0)t}) and V = span({(0, 1, 1)t}) be subspaces of
R3. Find the matrix B representing the projection onto V parallel to U.

Homework Equations





The Attempt at a Solution



If a matrix C with range U and and a matrix D whose nullspace is V then we can find the projection of matrix B

B = C(DC)−1D

Is my thought correct?
 
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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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