format rational A=[2 -1 4 -5 19; -1 3 -2 -1 -18; 0 1 5 -6 12; 3 -8 1 0 29] A = 2 -1 4 -5 19 -1 3 -2 -1 -18 0 1 5 -6 12 3 -8 1 0 29 A(1,:)=A(1,:)+A(2,:) A = 1 2 2 -6 1 -1 3 -2 -1 -18 0 1 5 -6 12 3 -8 1 0 29 A(2,:)=A(2,:)+A(1,:) A = 1 2 2 -6 1 0 5 0 -7 -17 0 1 5 -6 12 3 -8 1 0 29 A(4,:)=A(4,:)-3*A(1,:) A = 1 2 2 -6 1 0 5 0 -7 -17 0 1 5 -6 12 0 -14 -5 18 26 A(2,:)=A(2,:)-4*A(3,:) A = 1 2 2 -6 1 0 1 -20 17 -65 0 1 5 -6 12 0 -14 -5 18 26 A(3,:)=A(2,:)-A(3,:) A = 1 2 2 -6 1 0 1 -20 17 -65 0 0 -25 23 -77 0 -14 -5 18 26 A(4,:)=A(2,:)+14*A(2,:) A = 1 2 2 -6 1 0 1 -20 17 -65 0 0 -25 23 -77 0 15 -300 255 -975 A(4,:)=A(2,:)-14*A(2,:) A = 1 2 2 -6 1 0 1 -20 17 -65 0 0 -25 23 -77 0 -13 260 -221 845 A = A = ↑ {Error: Invalid expression. Check for missing or extra characters. } A = Aog A = 2 -1 4 -5 19 -1 3 -2 -1 -18 0 1 5 -6 12 3 -8 1 0 29 A(1,:)=A(1,:)+A(2,:) A = 1 2 2 -6 1 -1 3 -2 -1 -18 0 1 5 -6 12 3 -8 1 0 29 A(2,:)=A(2,:)+A(1,:) A = 1 2 2 -6 1 0 5 0 -7 -17 0 1 5 -6 12 3 -8 1 0 29 A(4,:)=A(4,:)-3*A(1,:) A = 1 2 2 -6 1 0 5 0 -7 -17 0 1 5 -6 12 0 -14 -5 18 26 Aog2=a {Undefined function or variable 'a'. } Aog2=A Aog2 = 1 2 2 -6 1 0 5 0 -7 -17 0 1 5 -6 12 0 -14 -5 18 26 A(2,:)=A(2,:)-4*A(3,:) A = 1 2 2 -6 1 0 1 -20 17 -65 0 1 5 -6 12 0 -14 -5 18 26 A(3,:)=A(2,:)-A(3,:) A = 1 2 2 -6 1 0 1 -20 17 -65 0 0 -25 23 -77 0 -14 -5 18 26 A(4,:)=A(4,:)+14*A(2,:) A = 1 2 2 -6 1 0 1 -20 17 -65 0 0 -25 23 -77 0 0 -285 256 -884 Aog3=A Aog3 = 1 2 2 -6 1 0 1 -20 17 -65 0 0 -25 23 -77 0 0 -285 256 -884 A(3,:)=A(3,:)/-25 A = 1 2 2 -6 1 0 1 -20 17 -65 0 0 1 -23/25 77/25 0 0 -285 256 -884 A(4,:)=A(4,:)+285*A(3,:) A = 1 2 2 -6 1 0 1 -20 17 -65 0 0 1 -23/25 77/25 0 0 0 -31/5 -31/5 A(4,:)=A(4,:)*5 A = 1 2 2 -6 1 0 1 -20 17 -65 0 0 1 -23/25 77/25 0 0 0 -31 -31 A(4,:)=A(4,:)/-31 A = 1 2 2 -6 1 0 1 -20 17 -65 0 0 1 -23/25 77/25 0 0 0 1 1 Aref=A Aref = 1 2 2 -6 1 0 1 -20 17 -65 0 0 1 -23/25 77/25 0 0 0 1 1 A(1,:)=A(1,:)-2*A(2,:) A = 1 0 42 -40 131 0 1 -20 17 -65 0 0 1 -23/25 77/25 0 0 0 1 1 A(1,:)=A(1,:)-42*A(3,:) A = 1 0 0 -34/25 41/25 0 1 -20 17 -65 0 0 1 -23/25 77/25 0 0 0 1 1 A(2,:)=A(2,:)-20*A(3,:) A = 1 0 0 -34/25 41/25 0 1 -40 177/5 -633/5 0 0 1 -23/25 77/25 0 0 0 1 1 A(2,:)=A(2,:)+20*A(3,:) A = 1 0 0 -34/25 41/25 0 1 -20 17 -65 0 0 1 -23/25 77/25 0 0 0 1 1 A(2,:)=A(2,:)+20*A(3,:) A = 1 0 0 -34/25 41/25 0 1 0 -7/5 -17/5 0 0 1 -23/25 77/25 0 0 0 1 1 A(1,:)=A(1,:)+(34/25)*A(5,:) {Index in position 1 exceeds array bounds (must not exceed 4). } A(1,:)=A(1,:)+(34/25)*A(4,:) A = 1 0 0 * 3 0 1 0 -7/5 -17/5 0 0 1 -23/25 77/25 0 0 0 1 1 A(2,:)=A(2,:)+(7/5)*A(4,:) A = 1 0 0 * 3 0 1 0 * -2 0 0 1 -23/25 77/25 0 0 0 1 1 A(3,:)=A(3,:)+(23/5)*A(4,:) A = 1 0 0 * 3 0 1 0 * -2 0 0 1 92/25 192/25 0 0 0 1 1 A(3,:)=A(3,:)-(23/5)*A(4,:) A = 1 0 0 * 3 0 1 0 * -2 0 0 1 -23/25 77/25 0 0 0 1 1 A(3,:)=A(3,:)-(23/5)*A(4,:) A = 1 0 0 * 3 0 1 0 * -2 0 0 1 -138/25 -38/25 0 0 0 1 1 A(3,:)=A(3,:)+(23/5)*A(4,:) A = 1 0 0 * 3 0 1 0 * -2 0 0 1 -23/25 77/25 0 0 0 1 1 A(3,:)=A(3,:)-(23/5)*A(4,:) A = 1 0 0 * 3 0 1 0 * -2 0 0 1 -138/25 -38/25 0 0 0 1 1 A(3,:)=A(3,:)+(23/5)*A(4,:) A = 1 0 0 * 3 0 1 0 * -2 0 0 1 -23/25 77/25 0 0 0 1 1 A(3,:)=A(3,:)+(23/25)*A(4,:) A = 1 0 0 * 3 0 1 0 * -2 0 0 1 * 4 0 0 0 1 1 Aans=A Aans = 1 0 0 * 3 0 1 0 * -2 0 0 1 * 4 0 0 0 1 1 diary off rref(Aog) ans = 1 0 0 0 3 0 1 0 0 -2 0 0 1 0 4 0 0 0 1 1 diary off format rational A=[-2 1 9 1; 3 3 -4 2; 1 4 5 5] A = Columns 1 through 3 -2 1 9 3 3 -4 1 4 5 Column 4 1 2 5 Asave=A Asave = Columns 1 through 3 -2 1 9 3 3 -4 1 4 5 Column 4 1 2 5 a=A a = Columns 1 through 3 -2 1 9 3 3 -4 1 4 5 Column 4 1 2 5 a([1 3],:)=a([3 1],:) a = Columns 1 through 3 1 4 5 3 3 -4 -2 1 9 Column 4 5 2 1 a(2,:)=a(2,:)-3+a(1,:) a = Columns 1 through 3 1 4 5 1 4 -2 -2 1 9 Column 4 5 4 1 a(2,:)=a(2,:)+3-a(1,:) a = Columns 1 through 3 1 4 5 3 3 -4 -2 1 9 Column 4 5 2 1 a(2,:)=a(2,:)-3*a(1,:) a = Columns 1 through 3 1 4 5 0 -9 -19 -2 1 9 Column 4 5 -13 1 a(3,:)=a(3,:)+2*a(1,:) a = Columns 1 through 3 1 4 5 0 -9 -19 0 9 19 Column 4 5 -13 11 a(2,:)=a(2,:)/-9 a = Columns 1 through 3 1 4 5 0 1 19/9 0 9 19 Column 4 5 13/9 11 a(3,:)=a(3,:)-9*a(2,:) a = Columns 1 through 3 1 4 5 0 1 19/9 0 0 0 Column 4 5 13/9 -2 ref2=a ref2 = Columns 1 through 3 1 4 5 0 1 19/9 0 0 0 Column 4 5 13/9 -2 a=[2 3 -4 1 2; 3 -1 -1 2 4; 1 -7 5 -1 6] a = Columns 1 through 3 2 3 -4 3 -1 -1 1 -7 5 Columns 4 through 5 1 2 2 4 -1 6 a([1 3],:)=a([3 1],:) a = Columns 1 through 3 1 -7 5 3 -1 -1 2 3 -4 Columns 4 through 5 -1 6 2 4 1 2 a(2,:)=a(2,:)-3*a(1,:) a = Columns 1 through 3 1 -7 5 0 20 -16 2 3 -4 Columns 4 through 5 -1 6 5 -14 1 2 a(3,:)=a(3,:)-2*a(1,:) a = Columns 1 through 3 1 -7 5 0 20 -16 0 17 -14 Columns 4 through 5 -1 6 5 -14 3 -10 a(2,:)=a(2,:)/20 a = Columns 1 through 3 1 -7 5 0 1 -4/5 0 17 -14 Columns 4 through 5 -1 6 1/4 -7/10 3 -10 a(3,:)=a(3,:)-17*a(2,:) a = Columns 1 through 3 1 -7 5 0 1 -4/5 0 0 -2/5 Columns 4 through 5 -1 6 1/4 -7/10 -5/4 19/10 a(3,:)=a(3,:)*(-5/2) a = Columns 1 through 3 1 -7 5 0 1 -4/5 0 0 1 Columns 4 through 5 -1 6 1/4 -7/10 25/8 -19/4 A=[2 3 -4 1 2; 3 -1 -1 2 4; 1 -7 5 -1 6] A = Columns 1 through 3 2 3 -4 3 -1 -1 1 -7 5 Columns 4 through 5 1 2 2 4 -1 6 rref(A) ans = Columns 1 through 3 1 0 0 0 1 0 0 0 1 Columns 4 through 5 21/8 -7/4 11/4 -9/2 25/8 -19/4 a a = Columns 1 through 3 1 -7 5 0 1 -4/5 0 0 1 Columns 4 through 5 -1 6 1/4 -7/10 25/8 -19/4 a(1,:)=a(1,:)+7*a(2,:) a = Columns 1 through 3 1 0 -3/5 0 1 -4/5 0 0 1 Columns 4 through 5 3/4 11/10 1/4 -7/10 25/8 -19/4 a(1,:)=a(1,:)+(3/5)*a(3,:) a = Columns 1 through 3 1 0 * 0 1 -4/5 0 0 1 Columns 4 through 5 21/8 -7/4 1/4 -7/10 25/8 -19/4 a(2,:)=a(2,:)+(4/5)*a(3,:) a = Columns 1 through 3 1 0 * 0 1 * 0 0 1 Columns 4 through 5 21/8 -7/4 11/4 -9/2 25/8 -19/4 rref(A) ans = Columns 1 through 3 1 0 0 0 1 0 0 0 1 Columns 4 through 5 21/8 -7/4 11/4 -9/2 25/8 -19/4 rref3=a rref3 = Columns 1 through 3 1 0 * 0 1 * 0 0 1 Columns 4 through 5 21/8 -7/4 11/4 -9/2 25/8 -19/4 rref3a=a rref3a = Columns 1 through 3 1 0 * 0 1 * 0 0 1 Columns 4 through 5 21/8 -7/4 11/4 -9/2 25/8 -19/4 delete rref3 [Warning: File 'rref3' not found.] remove rref3 {Undefined function 'remove' for input arguments of type 'char'. } a=[2 3 -4 4; 8 11 -7 8; 2 2 -4 -3] a = Columns 1 through 3 2 3 -4 8 11 -7 2 2 -4 Column 4 4 8 -3 A=a A = Columns 1 through 3 2 3 -4 8 11 -7 2 2 -4 Column 4 4 8 -3 rref(A) ans = Columns 1 through 3 1 0 0 0 1 0 0 0 1 Column 4 -157/18 7 -1/9 a a = Columns 1 through 3 2 3 -4 8 11 -7 2 2 -4 Column 4 4 8 -3 a(1,:)=a(1,:)/2 a = Columns 1 through 3 1 3/2 -2 8 11 -7 2 2 -4 Column 4 2 8 -3 a(2,:)=a(2,:)-8*a(1,:) a = Columns 1 through 3 1 3/2 -2 0 -1 9 2 2 -4 Column 4 2 -8 -3 a(3,:)=a(3,:)-2*a(1,:) a = Columns 1 through 3 1 3/2 -2 0 -1 9 0 -1 0 Column 4 2 -8 -7 a(2,:)=a(2,:)/-1 a = Columns 1 through 3 1 3/2 -2 0 1 -9 0 -1 0 Column 4 2 8 -7 a(3,:)=a(3,:)+1*a(2,:) a = Columns 1 through 3 1 3/2 -2 0 1 -9 0 0 -9 Column 4 2 8 1 a(3,:)=a(3,:)/-9 a = Columns 1 through 3 1 3/2 -2 0 1 -9 0 0 1 Column 4 2 8 -1/9 a(1,:)=a(1,:)-(3/2)*a(2,:) a = Columns 1 through 3 1 0 23/2 0 1 -9 0 0 1 Column 4 -10 8 -1/9 a(2,:)=a(2,:)+9*a(3,:) a = Columns 1 through 3 1 0 23/2 0 1 0 0 0 1 Column 4 -10 7 -1/9 a(1,:)=a(1,:)-(23/2)*a(3,:) a = Columns 1 through 3 1 0 0 0 1 0 0 0 1 Column 4 -157/18 7 -1/9 rref3b=a rref3b = Columns 1 through 3 1 0 0 0 1 0 0 0 1 Column 4 -157/18 7 -1/9 diary off