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Not a Linear Combination

LINALG-XBGHIZ

Which of the following statements are FALSE?

$(i)$ $2 x^2 +3x^3 -2 x^4$ is a linear combination of $x^2, x^3, x^4$

$(ii)$ $3 x^2-x+1$ is a linear combination of $x^2, x, 1$

$(iii)$ $\sqrt x+{1\over 3} y$ is a linear combination of $x$ and $y$

$(iv)$ $\sin x+ \cos y$ is a linear combination of $x$ and $y$

A

All of the above are false.

B

None of the above are false.

C

Statement $(iii)$ is false. The other statements are true.

D

Statement $(iv)$ is false. The other statements are true.

E

Statements $(iii)$ and $(iv)$ are false. The other statements are true.