# Is Wolfram Alpha linear independence wrong or am I missing something?

Maybe it's because you can't ask those questions to wolfram & I should use a matrix instead but when imputting

linear independence {$t$, $t^2+1$, $t^2+1-t$}

It says the three functions are linearly independent when the third one is clearly a linear combination of the other two. How should I input this to get a valid answer? I wanna check whether or not my results are correct.

• Entering linear independence {t, t, t} also gives (t,t,t) is linearly independent. Commented Aug 11, 2016 at 7:50
• linear independence {(0, 1, 0), (1, 0, 1), (1, -1, 1)}
– msm
Commented Aug 11, 2016 at 7:55
• This kind of problem is the price to pay if you use some more or less guessed pseudo-syntax, in which brackets have no proper fixed meaning. Wolfram|Alpha is a very useful tool, but don't forget it's more a google than a CAS. Commented Aug 11, 2016 at 9:48
• @leftaroundabout what a nice, polite way of saying "rtfm" :-) Commented Aug 11, 2016 at 11:21
• @Carl: There's an m?
– user14972
Commented Aug 11, 2016 at 15:34

It's because WolframAlpha interprets your input as one vector, i.e. the space of the single vector $(t, t^2+1, t^2+1-t)$.

An appropriate input would be (treating $1$, $t$ and $t^2$ as basis vectors):

linear independence (0,1,0), (1,0,1), (1,-1,1)

which outputs linearly dependent.

You can find other input examples for linear algebra here.

• Ah, I see now thank you for your answer. Commented Aug 11, 2016 at 8:07
• Can wolfram only do polynimials? What if I want to check the linear dependence of $\{ \sin x, x \}$ for example?
– Ovi
Commented Aug 11, 2016 at 15:45

Another way to check for linear independence in W|A is to compute the Wronskian, say with the input "wronskian(($t$, $t^2+1$, $t^2+1-t$), $t$)", which results in $0$ so the set of functions is indeed linearly dependent.