(%i1) "Einf. Determinante"$ (%i2) M1: matrix([1.0,0.0,1.0],[0.0,1.0,1.0],[0.0,0.0,1.0]); [ 1.0 0.0 1.0 ] [ ] (%o2) [ 0.0 1.0 1.0 ] [ ] [ 0.0 0.0 1.0 ] (%i3) determinant(M1); (%o3) 1.0 (%i4) M3: matrix([1.0,3.0,1.0],[2.0,6.0,1.0],[0.0,0.0,1.0]); [ 1.0 3.0 1.0 ] [ ] (%o4) [ 2.0 6.0 1.0 ] [ ] [ 0.0 0.0 1.0 ] (%i5) determinant(M3); (%o5) 0.0 (%i6) M4: matrix([1.0,3.0,1.0],[2.0,4.0,1.0],[0.0,0.0,0.0]); [ 1.0 3.0 1.0 ] [ ] (%o6) [ 2.0 4.0 1.0 ] [ ] [ 0.0 0.0 0.0 ] (%i7) determinant(M4); (%o7) 0.0 (%i8) M2: matrix([1.0,3.0,1.0],[2.0,1.0,1.0],[0.0,2.0,1.0]); [ 1.0 3.0 1.0 ] [ ] (%o8) [ 2.0 1.0 1.0 ] [ ] [ 0.0 2.0 1.0 ] (%i9) determinant(M2); (%o9) - 3.0 (%i10) M2a: matrix([1.0,3.0],[2.0,1.0]); [ 1.0 3.0 ] (%o10) [ ] [ 2.0 1.0 ] (%i11) determinant(M2a); (%o11) - 5.0 (%i12) M2b: matrix([1.0,3.0],[0.0,2.0]); [ 1.0 3.0 ] (%o12) [ ] [ 0.0 2.0 ] (%i13) determinant(M2b); (%o13) 2.0 (%i14) M2c: matrix([2.0,1.0],[0.0,2.0]); [ 2.0 1.0 ] (%o14) [ ] [ 0.0 2.0 ] (%i15) determinant(M2c); (%o15) 4.0 (%i16) determinant(M2a) - determinant(M2b) + determinant(M2c); (%o16) - 3.0 (%i17) "Aufbau des Normalenvektors"$ (%i18) "( det(M2c) , -det(M2b) , det(M2a) )^T "$ [ det(M2c) ] [ ] [ - det(M2b) ] [ ] [ det(M2a) ] (%i19) "Normalenvektor Vektor n1"$ (%i20) n1: transpose(matrix ([4.0,-2.0,-5.0])); [ 4.0 ] [ ] (%o20) [ - 2.0 ] [ ] [ - 5.0 ] (%i21) "Vektor a"$ (%i22) a: transpose(matrix ([1.0,2.0,0.0])); [ 1.0 ] [ ] (%o22) [ 2.0 ] [ ] [ 0.0 ] (%i23) "Vektor b"$ (%i24) b: transpose(matrix ([3.0,1.0,2.0])); [ 3.0 ] [ ] (%o24) [ 1.0 ] [ ] [ 2.0 ] (%i25) "Skalarprodukt zwischen den Vektoren : <a,n1> = 0.0"$ (%i26) "Skalarprodukt zwischen den Vektoren : <b,n1> = 0.0"$ (%i27) "Kreuzprodukt a x b"$ (%i28) a_b : transpose(matrix ([4.0,-2.0,-5.0])); [ 4.0 ] [ ] (%o28) [ - 2.0 ] [ ] [ - 5.0 ]