Hi @SineoftheTime

@Pizza sup

How is it going?

fine, how about you?

Pretty good

what courses are you following?

so you're studying multivariable calculus?

Yes

nice

Suppose i have 3 balls of colour red 2 balls of blue kai 1 white ball. How many combinations of 3 balls exist order doesnt matter.

@SineoftheTime did you do anything about algebra and geometry?

yes

by algebra I think you mean linear algebra

you can take a look at what I sent above (if you want)

@SineoftheTime yes

what message are you referring to?

Where I said hi to you, there is another my message above, above again

The one where I wrote "consider the Vector space" etc

ok let me take a look

Thank you!

the determinant should be $2k^2-k$

@SineoftheTime oh yes I checked now

so if $k^2-k=0$, the three vectors don't form a basis

Ok but the next steps shouldn't change right?

I don't understand what you're trying to do if $\det \neq 0$

Wait so I also have to consider when k is different from 1/2

right

@SineoftheTime I mean that if k is different from 0 or 1/2 then the determinant can never be 0

yes

so you have a basis

and therefore I can do what is written next, right?

you don't need to check if the span $\Bbb R^3$

@SineoftheTime $\text{basis means}$: spans entire space & linearly indepdnent?

its wrong?

since you have 3 linearly independent vectors, you already know thay span $\Bbb R^3$

no it's correct

aaaaaaa

using this

yes

but as you said "since you have 3 linearly independent vectors, you already know thay span $\Bbb R^3$"

so i can say this : they are linearly independent and span space.

yep