Let $v_{1} =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 2 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 1 5
, $v_{2} =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 6 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 2 15
, $v_{3} =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 19 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 7 45
and $w=$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ 4 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 7 8
.

$1.$ Is $w$ in $\left\{ v_{1},v_{2},v_{3} \right\}$? Type "yes" or "no".

$2.$ How many vectors are in $\left\{ v_{1},v_{2},v_{3} \right\}$? Enter "inf" if the answer is infinitely many.

$3.$ How many vectors are in $Span\left\{ v_{1},v_{2},v_{3} \right\}$? Enter "inf" if the answer is infinitely many.

$4.$ Is $w$ in the subspace spanned by $\left\{ v_{1},v_{2},v_{3} \right\}$? Type "yes" or "no".

You can earn partial credit on this problem.