Linear dependence or independence $\{ x,|x|\}$ over field $F=R,$ set of real numbers.
$|x|$ curve is V shaped curve while x is linear with slope $45^o$. When both curves are parallel or same, then linearly dependent else linearly independent.
Pls correct me with respect to following:
1)$\{ x,|x|\}$ is Linearly independent if domain is R (correct me if i am wrong in these statements) 2)$\{ x,|x|\}$ is Linearly independent if domain is $[-1,1]$ 3)$\{ x,|x|\}$ is Linearly independent if domain is $[-\infty, 0]$ ---> is this correct??? 4)$\{ x,|x|\}$ is Linearly dependent if domain is $[0,\infty]$