1.ya.20 Linear spaces

condition: Find the basis and dimension of the linear space \( L_{1} \) generated by the vectors \( \overline{a_{1}}, \overline{a_{2}}, \ldots \), basis and dimension of the linear space \( L_{2} \) generated vectors \( \overline{b_{1}}, \overline{b_{2}}, \ldots \), as well as basis and dimension \( L_{1}+L_{2} \) and dimension \( L_{1} \cap L_{2} \). a) \( \overline{a_{1}}=(-21,2,18), \overline{a_{2}}=(-7,-8,4), \overline{a_{3}}=(8,3,-6) \); \( \overline{b_{1}}=(-5,-1,3), \overline{b_{2}}=(-6,2,0), \overline{b_{3}}=(2,-1,2) \). b) \( \overline{a_{1}}=(27,-10,-14,-2), \overline{a_{2}}=(2.5,-10,-23) \), \( \overline{a_{3}}=(5,-9,4,21), \overline{a_{4}}=(-16,-13,-9,4) \), \( \overline{b_{1}}=(14,14,-16,-18), \overline{b_{2}}=(-8,-10,9,13) \), \( \overline{b_{3}}=(-10,-11,12,14)\).