Determine which of the following pairs of functions are linearly independent.

NO_ANSWER Linearly independent Linearly dependent  1. $f(\theta) = \cos(3\theta)\quad,\quad g(\theta)=2\cos^3(\theta)-2\cos(\theta)$

NO_ANSWER Linearly independent Linearly dependent  2. $f(t) = 3t \quad, \quad g(t) = |t|$

NO_ANSWER Linearly independent Linearly dependent  3. $f(x) = x^2\quad, \quad g(x) = 4|x|^2$

NO_ANSWER Linearly independent Linearly dependent  4. $f(\theta) = \cos(3\theta) \quad,\quad g(\theta)=2\cos^3(\theta)-4\cos(\theta)$

NO_ANSWER Linearly independent Linearly dependent  5. $f(t) = 2t^2+14t \quad,\quad g(t)=2t^2-14t$

NO_ANSWER Linearly independent Linearly dependent  6. $f(t)=e^{\lambda t}\cos(\mu t)\quad,\quad g(t)=e^{\lambda t}\sin(\mu t)\quad,\mu\ne 0$

NO_ANSWER Linearly independent Linearly dependent  7. $f(t)=17t^3 \quad, \quad g(t)=e^x$

NO_ANSWER Linearly independent Linearly dependent  8. $f(x) = x^3\quad , \quad g(x)=|x|^3$

NO_ANSWER Linearly independent Linearly dependent  9. $f(x, y)= 2 x - 4 y - 12,\quad g(x, y)= -3 x + 6 y +18$