4 beams > A := matrix( [ [w1+w2,-w2,0], [-w2,w2+w3,-w3], [0,-w3,w3+w0] ] ) ; [w1 + w2 -w2 0 ] [ ] A := [ -w2 w2 + w3 -w3 ] [ ] [ 0 -w3 w3 + w0] > inverse(A); [w2 w3 + w2 w0 + w3 w0 w2 (w3 + w0) w2 w3] [--------------------- , ------------ , -----] [ %1 %1 %1 ] [ ] [w2 (w3 + w0) (w1 + w2) (w3 + w0) (w1 + w2) w3] [------------ , ------------------- , ------------] [ %1 %1 %1 ] [ ] [w2 w3 (w1 + w2) w3 w1 w2 + w1 w3 + w2 w3] [----- , ------------ , ---------------------] [ %1 %1 %1 ] %1 := w1 w2 w3 + w1 w2 w0 + w1 w3 w0 + w2 w3 w0 > A := matrix( [ [a,-w2,0], [-w2,b,-w3], [0,-w3,c] ] ) ; [ a -w2 0 ] [ ] A := [-w2 b -w3] [ ] [ 0 -w3 c ] > inverse(A); [ 2 ] [b c - w3 w2 c w2 w3 ] [--------- ---- ----- ] [ %1 %1 %1 ] [ ] [ w2 c a c a w3 ] [ ---- --- ---- ] [ %1 %1 %1 ] [ ] [ 2] [ w2 w3 a w3 a b - w2 ] [ ----- ---- ---------] [ %1 %1 %1 ] 2 2 %1 := a b c - a w3 - w2 c 6 beams > A := matrix( [ [w1+w2,-w2,0, 0, 0], [-w2,w2+w3,-w3, 0, 0], [0,-w3,w3+w4, -w4 , 0],[0,0,-w4, w4+w5,-w5],[0,0,0,-w5,w5+w0] ] ) ; [w1 + w2 -w2 0 0 0 ] [ ] [ -w2 w2 + w3 -w3 0 0 ] [ ] A := [ 0 -w3 w3 + w4 -w4 0 ] [ ] [ 0 0 -w4 w4 + w5 -w5 ] [ ] [ 0 0 0 -w5 w5 + w0] > inverse(A); [w2 w4 w3 w5 + w2 w3 w4 w0 + w2 w3 w5 w0 + w2 w5 w4 w0 + w5 w4 w0 w3 (w4 w3 w5 + w3 w4 w0 + w3 w5 w0 + w5 w4 w0) w2 w2 w3 (w4 w5 + w4 w0 + w5 w0) w3 w2 w4 (w5 + w0) w2 w4 w3 w5] [------------------------------------------------------------------- , ---------------------------------------------- , ----------------------------- , ------------------ , -----------] [ %1 %1 %1 %1 %1 ] [(w4 w3 w5 + w3 w4 w0 + w3 w5 w0 + w5 w4 w0) w2 w2 w4 w3 w5 + w2 w3 w4 w0 + w2 w3 w5 w0 + w2 w5 w4 w0 + w1 w4 w3 w5 + w3 w4 w1 w0 + w3 w1 w5 w0 + w1 w5 w4 w0 [---------------------------------------------- , ------------------------------------------------------------------------------------------------------------- , [ %1 %1 w3 (w2 w4 w5 + w2 w4 w0 + w2 w5 w0 + w1 w4 w5 + w4 w1 w0 + w1 w5 w0) w3 w4 (w2 w5 + w2 w0 + w1 w5 + w1 w0) w4 w3 w5 (w1 + w2)] -------------------------------------------------------------------- , ------------------------------------- , ------------------] %1 %1 %1 ] [w2 w3 (w4 w5 + w4 w0 + w5 w0) w3 (w2 w4 w5 + w2 w4 w0 + w2 w5 w0 + w1 w4 w5 + w4 w1 w0 + w1 w5 w0) [----------------------------- , -------------------------------------------------------------------- , [ %1 %1 w2 w4 w3 w5 + w2 w3 w4 w0 + w2 w3 w5 w0 + w2 w1 w4 w5 + w2 w4 w1 w0 + w2 w1 w5 w0 + w1 w4 w3 w5 + w3 w4 w1 w0 + w3 w1 w5 w0 w4 (w2 w3 w5 + w2 w3 w0 + w2 w1 w5 + w1 w2 w0 + w3 w1 w5 + w1 w3 w0) --------------------------------------------------------------------------------------------------------------------------- , -------------------------------------------------------------------- , %1 %1 w4 w5 (w1 w2 + w1 w3 + w2 w3)] -----------------------------] %1 ] [w3 w2 w4 (w5 + w0) w3 w4 (w2 w5 + w2 w0 + w1 w5 + w1 w0) w4 (w2 w3 w5 + w2 w3 w0 + w2 w1 w5 + w1 w2 w0 + w3 w1 w5 + w1 w3 w0) [------------------ , ------------------------------------- , -------------------------------------------------------------------- , [ %1 %1 %1 w2 w4 w3 w5 + w2 w3 w4 w0 + w2 w3 w1 w5 + w2 w1 w3 w0 + w2 w1 w4 w5 + w2 w4 w1 w0 + w1 w4 w3 w5 + w3 w4 w1 w0 w5 (w1 w2 w3 + w2 w1 w4 + w3 w2 w4 + w1 w3 w4)] ------------------------------------------------------------------------------------------------------------- , ----------------------------------------------] %1 %1 ] [w2 w4 w3 w5 w4 w3 w5 (w1 + w2) w4 w5 (w1 w2 + w1 w3 + w2 w3) w5 (w1 w2 w3 + w2 w1 w4 + w3 w2 w4 + w1 w3 w4) w2 w4 w3 w5 + w1 w3 w2 w4 + w2 w3 w1 w5 + w2 w1 w4 w5 + w1 w4 w3 w5] [----------- , ------------------ , ----------------------------- , ---------------------------------------------- , -------------------------------------------------------------------] [ %1 %1 %1 %1 %1 ] %1 := w2 w1 w4 w3 w5 + w2 w3 w4 w1 w0 + w2 w5 w4 w0 w3 + w2 w3 w1 w5 w0 + w2 w1 w5 w4 w0 + w1 w5 w4 w0 w3 > A := matrix( [ [a,-w2,0, 0, 0], [-w2,b,-w3, 0, 0], [0,-w3,c, -w4 , 0],[0,0,-w4, d,-w5],[0,0,0,-w5,e] ] ) ; [ a -w2 0 0 0 ] [ ] [-w2 b -w3 0 0 ] [ ] A := [ 0 -w3 c -w4 0 ] [ ] [ 0 0 -w4 d -w5] [ ] [ 0 0 0 -w5 e ] > inverse(A); [ 2 2 2 2 2 2 2 2 ] [w3 w5 - w3 d e - e b w4 - w5 b c + e d b c w2 (-e w4 - w5 c + e c d) w2 w3 (-w5 + d e) e w2 w4 w3 w4 w5 w3 w2] [----------------------------------------------- , --------------------------- , ------------------ , ---------- , -----------] [ %1 %1 %1 %1 %1 ] [ ] [ 2 2 2 2 2 ] [w2 (-e w4 - w5 c + e c d) (-e w4 - w5 c + e c d) a a w3 (-w5 + d e) w4 e w3 a w4 w5 w3 a] [--------------------------- , -------------------------- , ----------------- , --------- , ----------] [ %1 %1 %1 %1 %1 ] [ ] [ 2 2 2 2 2 2 2 2 ] [w2 w3 (-w5 + d e) a w3 (-w5 + d e) -a b w5 + a d e b + w2 w5 - d e w2 w4 e (a b - w2 ) w4 w5 (a b - w2 )] [------------------ , ----------------- , -------------------------------------- , ---------------- , -----------------] [ %1 %1 %1 %1 %1 ] [ ] [ 2 2 2 2 2 ] [e w2 w4 w3 w4 e w3 a w4 e (a b - w2 ) e (a b c - a w3 - w2 c) w5 (a b c - a w3 - w2 c)] [---------- , --------- , ---------------- , ------------------------- , --------------------------] [ %1 %1 %1 %1 %1 ] [ ] [ 2 2 2 2 2 2 2 2] [w4 w5 w3 w2 w4 w5 w3 a w4 w5 (a b - w2 ) w5 (a b c - a w3 - w2 c) -a d w3 + a d b c - a w4 b - d w2 c + w4 w2 ] [----------- , ---------- , ----------------- , -------------------------- , ------------------------------------------------] [ %1 %1 %1 %1 %1 ] 2 2 2 2 2 2 2 2 2 2 %1 := a w3 w5 - a w3 d e - a e b w4 - a w5 b c + a e d b c + e w2 w4 + w5 w2 c - e d w2 c