Suppose $3_1+2_2−_3=_4$. Which of the following statements are true? $\newcommand{\span}{\text{span}}$
Question: Suppose $3_1+2_2−_3=_4$. Which of the following statements are true? ​​​​​​

$\span( {_1,_2,_3} ) = \span( {_1,_2,_3,_4} )$

$\span( {_1,_2,_4} ) = \span( {_1,_2,_3,_4} )$

$\span( {_1,_2,_3} )$ is contained in but not equal to $\span( {_1,_2,_3,_4} ).$

$\span( {_1,_2,_4} )$ is contained in but not equal to $\span( {_1,_2,_3,_4} ).$


I chose answers 1 and 2, but I am new to this topic so I am not entirely sure if it's correct.
Does $_3$ qualify as a valid linear combination of all vectors: $$ _3 = 3_1 + 2_2 - _4 + 0_3$$ AND/OR  $$ _3 = 6_1 + 4_2 - 2_4 - _3$$
If yes, then 2nd statment is true right?
Thank you!
The correct answer is the first one since the non trivial containment is due to the fact that you find a $\textbf{non trivial}$ combination of $u_{4}$, expressed as linearly dependant from $u_{1},u_{2},u_{3}$.
The correct answer is the first one since the non trivial containment is due to the fact that you find a $\textbf{non trivial}$ combination of $u_{4}$, expressed as linearly dependant from $u_{1},u_{2},u_{3}$.