Let $u$, $w$, $v_1$, $v_2$, and $v_3$ be the vectors in $\mathbb{R}^4$ defined by

$$u = \left[\begin{array}{c} 18\cr 1\cr -11\cr 9 \end{array}\right] \quad w = \left[\begin{array}{c} -7\cr -6\cr -23\cr -20 \end{array}\right] \quad v_1 = \left[\begin{array}{c} -12\cr 3\cr -12\cr 11 \end{array}\right] \quad v_2 = \left[\begin{array}{c} -3\cr 3\cr -4\cr 9 \end{array}\right] \quad v_3 = \left[\begin{array}{c} 11\cr 3\cr -11\cr 1 \end{array}\right]$$

(a) Is $u \in \mbox{span}\lbrace v_1, v_2, v_3 \rbrace$? Write all zeros if it is not in the span or write zero as a non-trivial (not all zero coefficients) linear combination of $u$, $v_1$, $v_2$, and $v_3$ if $u$ is in the span.

(b) Is $w \in \mbox{span}\lbrace v_1, v_2, v_3 \rbrace$? Write all zeros if it is not or if it is in the span write zero as a non-trivial (not all zero coefficients) linear combination of $w$, $v_1$, $v_2$, and $v_3$ if $w$ is in the span.

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