From 7a73162607544204032aa66cce755daf21edebda Mon Sep 17 00:00:00 2001 From: Matt Strapp Date: Tue, 24 May 2022 11:18:46 -0500 Subject: Graduate Signed-off-by: Matt Strapp --- math2373/lab2.txt | 1024 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1024 insertions(+) create mode 100644 math2373/lab2.txt (limited to 'math2373/lab2.txt') diff --git a/math2373/lab2.txt b/math2373/lab2.txt new file mode 100644 index 0000000..689a36b --- /dev/null +++ b/math2373/lab2.txt @@ -0,0 +1,1024 @@ +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 -- cgit v1.2.3