1.ya.18 Linear spaces

Condition: Vectors are given in linear space. \[ \begin{array}{l} \overrightarrow{c_{1}}=\left(\begin{array}{c} 3 A \\ 1 \\ B \\ 3 \end{array}\right) ; \overrightarrow{c_{2}}=\left(\begin{array}{c} A \\ 1 \\ -B \\ 2 \end{array}\right) ; \overrightarrow{c_{3}}=\left(\begin{array}{c} A \\ -1 \\ 3 B \\ -1 \end{array}\right) ; \overrightarrow{d_{1}}=\left(\begin{array}{c} 2 A \\ 3 \\ 3 B \\ 2 \end{array}\right) ; \\ \overrightarrow{d_{2}}=\left(\begin{array}{c} 2 A \\ 3 \\ B \\ 1 \end{array}\right) ; \overrightarrow{d_{3}}=\left(\begin{array}{c} B \\ 0 \end{array}\right) . \end{array} \] Let \( C \) be a linear space spanned by the first three vectors, \( D- \) by the last three. Find the dimension and basis vectors of the linear space: a) \( C \); b) \(C+D\); c) \( C \cap D \).