Subspace in R^4: Investigating (2x+3y, x, 0, 1) as a Potential Subspace

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Homework Statement



Is this a subspace of R^4, (2x+3y, x, 0 , 1) . Give reasons

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The Attempt at a Solution



I am completely stuck at this one
 
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A subset U of V is a subspace of V if it satisfies the properties needed to be a vector space: additive identity; closure under vector addition; closure under scalar multiplication.

Check that your given subset satisfies the properties.

a) Is there an additive identity from your set for R^4?

b) If you take two vectors from your given space, a and b, is a+b still in your set?

c) Is the scalar multiple of any vector in your set still in the set?
 
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You might want to look particularly at the fourth component in a scalar product such as 2v.
 

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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