Linearly Independency of functions

Question

Show if the functions are linearly independent

$x(t)=3$, $y(t)=3\sin^2t$, $z(t)= 4\cos^2t$

How can i show this?

Can you write out what you need to prove? – Git Gud Jul 02 '14 at 00:56 — Git Gud, Jul 02 '14 at 00:56
A related problem. – Mhenni Benghorbal Jul 02 '14 at 01:37 — Mhenni Benghorbal, Jul 02 '14 at 01:37

score 3 · Answer 1 · answered Jul 02 '14 at 00:57

3

$x(t) - y(t) - \frac{3}{4} z(t) = 0$ for all $t$, so they are not linearly independent.

answered Jul 02 '14 at 00:57

Hans Engler

score 1 · Answer 2 · answered Jul 02 '14 at 00:59

1

Hint: Knowing that $\sin^2t+\cos^2t=1$, it is obvious that $4y+3z=12$. Now multiply x with $-4$, and add it to the previous sum.

answered Jul 02 '14 at 00:59

Lucian

score 0 · Accepted Answer · answered Jul 02 '14 at 00:53

0

Can you compute the Wronskian?

answered Jul 02 '14 at 00:53

ncmathsadist

3 Answers3