Consider the vectors $,V_1=2t^2+t+2,V_2=t^2-2t$

$V_3=5t^2-5t+2,V_4=-t^2-3t-2in{P}_2$

$($x$)$ Find a basis of the vector space spanned by

$\{v_1,v_2,v_3,v_4\}$

$($b$)$ Determine it the vector $u=t^2+t+2$ belongs to the spar of $\{v_1,v_2,v_3,v_4\}$

$($c$)$ Determine it the set $\{V_1,V_2,V_3,V_4\}$ is a linearly independent subset of $P_2.$