How to determine a basis given a set of vectors?

dmitriylm
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Homework Statement


Let V be the subspace spanned by the following vectors:
[ 0]...[ 1 ]...[2]
[ 2]...[ 1 ]...[5]
[-1]...[3/4]...[0]

Determine a basis for V.



The Attempt at a Solution



I'm not quite sure how to start here. Would placing the vectors in a matrix and deriving its reduced echelon form give me a basis?
 
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dmitriylm said:

Homework Statement


Let V be the subspace spanned by the following vectors:
[ 0]...[ 1 ]...[2]
[ 2]...[ 1 ]...[5]
[-1]...[3/4]...[0]

Determine a basis for V.



The Attempt at a Solution



I'm not quite sure how to start here. Would placing the vectors in a matrix and deriving its reduced echelon form give me a basis?

Are these row vectors or column vectors?
 
Mark44 said:
Are these row vectors or column vectors?

These are column vectors.
 
If the three vectors are linearly independent, they are your basis. If they're linearly dependent, some subset of them will be your basis.
 

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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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