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Linear Algebra

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Moderate

Increasing Linear Combination

LINALG-4GZSNJ

Suppose that $F$is a linear combination of $x,y,z$. Holding $y,z$ constant if we increase the value of $x$ by $2$, we increase the value of $F$ by $3$.

Which of the following must be TRUE?

$(i)$ Holding, $x, y$ constant, if we increase the value of $z$ by $3$, then we increase the value of $F$ by $2$.

$(ii)$ Holding $y,z$ constant, if we increase the value of $x$ by $3$ then we increase the value of $F$ by $2$.

$(iii)$ If we decrease the value of $x$ by $2$, we would decrease the value of $F$ by $3$.

A

All of the above must be true.

B

None of the above must be true.

C

Only $(i)$ must be true.

D

Only $(ii)$ must be true.

E

Only $(iii)$ must be true.