maxima matrix (%i1 (%o1 (%i2 (%o2 matrix([1,2,3],[4,5,6],[7,8,9]; ( matrix([a,b,c,d],[e,f,g,h]; a b c d e f g h matrix [ ] ma

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1 maxima Contents ( Date: 2005/10/5. 1

2 maxima matrix (%i1 (%o1 (%i2 (%o2 matrix([1,2,3],[4,5,6],[7,8,9]; ( matrix([a,b,c,d],[e,f,g,h]; a b c d e f g h matrix [ ] matrix maxima maxima : (%i3 (%o3 (%i4 (%o4 A : matrix([1,2,3],[4,5,6],[7,8,9]; ( B : matrix([a,b,c,d],[e,f,g,h]; a b c d e f g h A, B A B A B (%i5 A; (%o (%i6 ( B; a b c d (%o6 e f g h 1.3. (. A A A1 (%i7 A1 : A; (%o (%i8 A1; (%o A A1 A A1 A1 A

3 maxima A C ( A maxima copymatrix : (%i9 C :copymatrix(a; (%o (%i10 C; (%o A C A C maxima + A, B, A1, C A, B maxima kill (%i11 kill(a, B, A1, C; (%o11 DONE (%i12 ( A : matrix([1,2],[3,4]; 1 2 (%o (%i13 ( B : matrix([a,b],[c,d]; a b (%o13 c d (%i14 ( C : A + B; a + 1 b + 2 (%o14 c + 3 d + 4 A B 2 2- A + B C (%i15 ( A + B; a + 1 b + 2 (%o15 c + 3 d (%i16 ( A. B; 2c + a 2d + b (%o16 4c + 3a 4d + 3b (%i17 ( D : matrix([a,b,c],[d,e,f]; a b c (%o17 d e f

4 4 (%i18 E : matrix([p,q],[r,s],[t,u]; p q (%o18 r s t u (%i19 ( F : D. E; ct + br + ap cu + bs + aq (%o19 ft + er + dp fu + es + dq 2 2- A, B AB 2 3- D 3 2- E DE F (%i20 D. A; incompatible dimensions - cannot multiply -- an error. Quitting. To debug this try DEBUGMODE(TRUE; * ( kill(all (%i21 kill(all; (%o0 DONE (%i1 ( A : matrix([a,b,c],[d,e,f]; a b c (%o1 d e f (%i2 ( B : 3 * A; 3a 3b 3c (%o2 3d 3e 3f A A maxima ˆˆ (%i3 kill(all; (%o0 DONE (%i1 A : matrix([2,3,4],[-1,0,3],[2,1,-2]; (%o (%i2 A^^3; (%o A 3 (%i3 A. A. A; (%o

5 maxima 5 ( maxima maxima transpose (%i4 A; (%o4 (%i5 (%o5 (%i6 (%o6 (%i7 (%o transpose(a; ( C : matrix([a,b,c],[d,e,f]; a b c d e f transpose(c; a d b e c f A maxima echelon (%i8 kill(all; (%o0 DONE (%i1 A : matrix([1,2,3],[4,5,6],[7,8,9]; (%o (%i2 echelon(a; (%o (%i3 B : matrix([1,2,3],[4,5,6],[7,8,0]; (%o (%i4 C : echelon(b; (%o maxima A echelon(a A (rank maxima rank (%i5 rank(a; (%o5 2 (%i6 rank(b;

6 6 (%o6 3 A, B n A n A A 1 maxima invert (%i7 (%o7 invert(b; invert (%i8 invert(a; Division by 0 -- an error. Quitting. To debug this try DEBUGMODE(TRUE; rank Aˆˆ(-1 A (%i9 (%o9 B^^(-1; A maxima determinant (%i10 determinant(a; (%o10 0 (%i11 determinant(b; (%o11 27 (%i12 determinant(b^^(-1; (%o

7 maxima i A[i] maxima row row(a,i (%i13 kill(all; (%o0 DONE (%i1 A : matrix([a,b,c],[d,e,f],[g,h,i]; (%o1 a b c d e f g h i (%i2 A[1]; (%o2 [a, b, c] (%i3 A[2]; (%o3 [d, e, f] (%i4 A[3]; (%o4 [g, h, i] (%i5 row(a,1; (%o5 ( a b c (%i6 row(a,2; (%o6 ( d e f (%i7 row(a,3; (%o7 ( g h i 2 A[i] row(a,i A[1] [a,b,c] a, b, c row(a,1 (a b c 1 3- A 2 2 (%i8 A[2] : 2 * A[2]; (%o8 [2d, 2e, 2f] (%i9 A; (%o9 a b c 2d 2e 2f g h i A 2 2 A A row A row(a,2 : (1/2 * row(a,2 (%i10 row(a,2 : (1/2 * row(a,2; Improper value assignment: ROW (A, 2 FALSEfalse -- an error. Quitting. To debug this try DEBUGMODE(TRUE; (%i11 A[2] : (1/2 * A[2]; (%o11 [d, e, f] (%i12 A;

8 8 (%o12 a b c d e f g h i A (%i13 A[1] : A[1] + 3 * A[2]; (%o13 [3d + a, 3e + b, 3f + c] (%i14 A; 3d + a 3e + b 3f + c (%o14 d e f g h i (%i15 A[1] : A[1] - 3 * A[2]; (%o15 [a, b, c] (%i16 A; (%o16 a b c d e f g h i A 1 1 B (%i17 B : A[1]; (%o17 [a, b, c] (%i18 A[1] : A[3]; (%o18 [g, h, i] (%i19 A[3] : B; (%o19 [a, b, c] (%i20 A; (%o20 g h i d e f a b c A i transpose(transpose(a[i] col(a[i] (%i21 kill(all; (%o0 DONE (%i1 A : matrix([r,s,t],[u,v,w],[x,y,z]; (%o1 r s t u v w x y z (%i2 transpose(transpose(a[1]; (%o2 (%i3 (%o3 r u x col(a,1; r u x

9 maxima 9 transpose(transpose(a[1] col(a, transpose A (i,j- A[i][j] A[i,j] (%i4 kill(all; (%o0 DONE (%i1 A : matrix([1,2,3,4],[5,6,7,8],[9,10,11,12]; (%o (%i2 A[2][3]; (%o2 7 (%i3 A[2,3]; (%o3 7 A (2,3 A (2,3 x? A[2][3] : x OK (%i4 A[2,3] : x; (%o4 x (%i5 A; (%o x A (3,2- y A[3,2] : y (%i6 A[3,2] : y; (%o6 y (%i7 A; (%o x 8 9 y maxima x + 2y + 3z = 4, 5x + 6y + 7z = 8, 9x + 10y + 11z = 0 maxima eq1 (%i8 kill(all; (%o0 DONE (%i1 eq1 : [x+2*y+3*z=4, 5*x+6*y+7*z=8, 9*x+10*y+11*z=12]; (%o1 [3z + 2y + x = 4, 7z + 6y + 5x = 8, 11z + 10y + 9x = 12] eq1 (x,y,z A maxima coefmatrix

10 10 (%i2 xx : [x,y,z]; (%o2 [x, y, z] (%i3 A : coefmatrix(eq1, xx; (%o xx [x,y,z] (%i3 A : coefmatrix([x+2*y+3*z=4, 5*x+6*y+7*z=8, 9*x+10*y+11*z=12],[x,y,x]; Ax = b (A b maxima augcoefmatrix (A b (A b (%i4 (%o4 Ab : augcoefmatrix(eq1, xx; rank(a rank(ab maxima (%i5 echelon(ab; (%o (%i6 rank(a; (%o6 2 (%i7 rank(ab; (%o7 2 rank(a = rank(ab = 2 eq1 n = 3 rank(a = = maxima eq1 maxima solve (%i8 solve(eq1, xx; Dependent equations eliminated: (3 (%o8 [[x = %R1 2, y = 3 2%R1, z = %R1]] %R1 solve (%i9 kill(all; (%o0 DONE

11 maxima 11 (%i1 eq2 : [x + 2*y = 3, 4*x + 5*y = 6, 7*x + 8*y = 0]; (%o1 [2y + x = 3, 5y + 4x = 6, 8y + 7x = 0] (%i2 xx : [x,y]; (%o2 [x, y] (%i3 solve(eq2, xx; Inconsistent equations: (1 -- an error. Quitting. To debug this try DEBUGMODE(TRUE; (%i4 A : coefmatrix(eq2, xx; (%o (%i5 Ab : augcoefmatrix(eq2, xx; (%o (%i6 echelon(ab; (%o (%i7 rank(a; (%o7 2 (%i8 rank(ab; (%o8 3 rank(a rank(ab eq2

12 12 3. maxima, maxima maxima

13 address: maxima 13

maxima Contents 1. 1.1. maxima 1.. maxima 1.3. maxima 3 1.4. maxima 5. 7 3. 10 3.1. 10 3.. 11 3.3. 1 4. 14 5. 16 5.1. 16 5.. 16 5.3. 17 5.4. 0 6. 6.1. 6.. 6 7. maxima 30 7.1. 30 7.. 34 7.3. 4 8. 45 8.1.

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