The dot product of two vectors in ${\mathbb R}^3$ is defined by $$\left\lbrack \begin{array}{c} a_1 \\ a_2 \\ a_3 \end{array} \right\rbrack \cdot \left\lbrack \begin{array}{c} b_1 \\ b_2 \\ b_3 \end{array} \right\rbrack = a_1 b_1 + a_2 b_2 + a_3 b_3.$$ Let $\vec{v}= \left[\begin{array}{c} -6\cr 6\cr -7 \end{array}\right]$. Find the matrix $A$ of the linear transformation from ${\mathbb R}^3$ to ${\mathbb R}$ given by $T(\vec{x}) = \vec{v} \cdot \vec{x}.$

$A =$ $\left[\Rule{0pt}{1.2em}{0pt}\right.$$\left]\Rule{0pt}{1.2em}{0pt}\right.$