Can a Set of 5 Vectors Span All of R6?

ykaire
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1. Can a set of 5 vectors in R6 span all of R6?I want to say that it does span, because i remember my teacher saying "don't think of the physical world," but I'm not entirely sure if it does.
 
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Neither of those are very good reasons for answering one way or another. Why do you think 5 vectors can span R^6?
 
Dick said:
Neither of those are very good reasons for answering one way or another. Why do you think 5 vectors can span R^6?


I'm not sure, to be honest.
 
How many vectors span R2? R3?
 
venom192 said:
How many vectors span R2? R3?
Um, I'm guessing that vectors span R2 and 3 Vectors span R3.
so... that must mean that 6 vectors span R6.
 
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Why are you doing all of this guessing? It looks to me like you need to review the basic definitions. You should know immediately that R6 has dimension 6. What does that mean. What can you say about any spanning set in a space of dimension n? What can you say about any linearly independent set in a space of dimension n?
 

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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