<prompt> Ruhusu M_2 mara 2 iwe nafasi ya vekta ya 2 mara 2 matrices halisi. HebuAkushotoanzasafucc1 na 2 -1 na 3mwishoarraykulia quad Bleftanzaarraycc2 1 0 na 4mwishosafukuliana ubainishe mabadiliko ya mstari L: M_2 mara 2 mshale wa kulia M_2 mara 2 by LXA X B. Kokotoa ufuatiliaji wa L.  <response>: Tambua M_2 mara 2 na mathbbR4 kupitiakushotoanzaarraylla b nc dmwishosafukulia leftrightarrowleftanzaarrayla nb nc ndmwishosafukuliana kutenganisha L katika kuzidisha mabadiliko mawili ya mstari,M_2 mara 2 simeq mathbbR4 stackrelL_Alongrightarrow mathbbR4 stackrelL_Blongrightarrow mathbbR4 simeq M_2 mara 2ambapo L_AXA X na L_BXX B. niNambari za mabadiliko haya mawili ya mstari kwa misingi ya kisheria ya mathbbR4L_Akushotoanzaarrayrrr1 0 2 0 n0 1 0 2 n-1 0 3 0 n0 -1 0 3mwishoarraykulia quad text na L_Bleftanzaarraylll2 0 0 0 n1 4 0 0 n0 0 2 0 n0 0 1 4mwishosafukuliakisha operatornamedet Loperatornamedet L_A cdot opereta jinadet L_B96223 cdot2 cdot 32 26 cdot 52, na kukokotoa ufuatiliaji wa L, tunahitaji tu vipengele vya mshazari vya L_A cdot L_B, yaani,jina la operetatr L2461224 maandishi . 