Find a basis for a set S of R4

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Homework Statement



Find a basis for the subspace S of vectors (A+B, A-B+2C, B, C) in R4

What is the dimension of S?

The Attempt at a Solution



Do I just plug in varying values for A B and C to create four vectors, and see if they are linearly independent? If they are then I've found a basis?
 
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Making any two of A, B & C zero results in a vector in S. How many such vectors are there?
 
Or, similar to voko's observation write it like this:$$
A(1,1,0,0)+B(1,-1,1,0)+C(0,2,0,1)$$and see if that helps.
 

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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