octave:2> A = [1 5 10 42; -1 -4 13 37; 3 7 24 8] A = 1 5 10 42 -1 -4 13 37 3 7 24 8 octave:3> [l,u,p] = lu(A) l = 1.00000 0.00000 0.00000 0.33333 1.00000 0.00000 -0.33333 -0.62500 1.00000 u = 3.00000 7.00000 24.00000 8.00000 0.00000 2.66667 2.00000 39.33333 0.00000 0.00000 22.25000 64.25000 p = 0 0 1 1 0 0 0 1 0 octave:4> a1 = A*[1;0;0] error: operator *: nonconformant arguments (op1 is 3x4, op2 is 3x1) error: evaluating binary operator `*' near line 4, column 7 error: evaluating assignment expression near line 4, column 4 octave:4> aa = A*[1;0;0] error: operator *: nonconformant arguments (op1 is 3x4, op2 is 3x1) error: evaluating binary operator `*' near line 4, column 7 error: evaluating assignment expression near line 4, column 4 octave:4> a1 = A*[1;0;0;0] a1 = 1 -1 3 octave:5> a2=A*[0;1;0;0] a2 = 5 -4 7 octave:6> a2 - a2[1]/a1[1]*a1 parse error: syntax error >>> a2 - a2[1]/a1[1]*a1 ^ octave:6> a2 - 5*a1 ans = 0 1 -8 octave:7> a1 a1 = 1 -1 3 octave:8> a2 a2 = 5 -4 7 octave:9> aa2=a2 - 5*a1 aa2 = 0 1 -8 octave:10> a3= A*[0;0;1;0] a3 = 10 13 24 octave:11> aa3 = a3 - 10*a1 aa3 = 0 23 -6 octave:12> a4 = A*[0;0;0;1] a4 = 42 37 8 octave:13> aa4 = a4 - 42*a1 aa4 = 0 79 -118 octave:14> [aa2; aa3; aa4] ans = 0 1 -8 0 23 -6 0 79 -118 octave:15> [aa2 aa3 aa4] ans = 0 0 0 1 23 79 -8 -6 -118 octave:16> aaa3 = aa3 - 23*aa2 aaa3 = 0 0 178 octave:17> aaa4 = aa4 + 118*aa2 aaa4 = 0 197 -1062 octave:18> aaa4 = aa4 - 79*aa2 aaa4 = 0 0 514 octave:19> [aaa3 aaa4] ans = 0 0 0 0 178 514 octave:20> aaaa4 = aaa4 - 514/178*aaa3 aaaa4 = 0 0 0 octave:21> [a1 aa2 aaa3] ans = 1 0 0 -1 1 0 3 -8 178 octave:22> L = [a1 aa2 aaa3] L = 1 0 0 -1 1 0 3 -8 178 octave:23> inv(L) ans = 1.00000 0.00000 0.00000 1.00000 1.00000 0.00000 0.02809 0.04494 0.00562 octave:24> U = inv(L)*A U = 1.00000 5.00000 10.00000 42.00000 0.00000 1.00000 23.00000 79.00000 0.00000 0.00000 1.00000 2.88764 octave:25> quit