Let $v_1$, $v_2$, $v_3$ be the vectors in $\mathbb{R}^3$ defined by

$$v_1 = \left[\begin{array}{c} -33\cr -27\cr -5 \end{array}\right] \quad v_2 = \left[\begin{array}{c} 11\cr 18\cr 1 \end{array}\right] \quad v_3 = \left[\begin{array}{c} -11\cr 9\cr -3 \end{array}\right]$$

(a) Is $\lbrace v_1, v_2, v_3 \rbrace$ linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a non-trivial (not all zero coefficients) linear combination of $v_1$, $v_2$, and $v_3$

(b) Is $\lbrace v_1, v_2 \rbrace$ linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a non-trivial (not all zero coefficients) linear combination of $v_1$ and $v_2$.

(c) Type the dimension of $\mbox{span}\lbrace v_1, v_2, v_3\rbrace$: