Let $$B = \left[\begin{array}{ccc} -7 &-4 &-6\cr 9 &7 &7\cr -4 &-4 &-3 \end{array}\right].$$ (a) Find the reduced row echelon form of the matrix $B$.
$\mathrm{rref}(B) =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$

(b) How many pivot columns does $B$ have?


(c) Do the vectors in the set $\left\lbrace \left[\begin{array}{c} -7\cr 9\cr -4 \end{array}\right], \left[\begin{array}{c} -4\cr 7\cr -4 \end{array}\right], \left[\begin{array}{c} -6\cr 7\cr -3 \end{array}\right] \right\rbrace$ span $\mathbb{R}^3$? Be sure you can explain and justify your answer.
choose the vectors span R^3 the vectors do not span R^3

(d) Are the vectors in the set $\left\lbrace \left[\begin{array}{c} -7\cr 9\cr -4 \end{array}\right], \left[\begin{array}{c} -4\cr 7\cr -4 \end{array}\right], \left[\begin{array}{c} -6\cr 7\cr -3 \end{array}\right] \right\rbrace$ linearly independent? Be sure you can explain and justify your answer.
choose linearly dependent linearly independent