week11

1123 days ago by wldnd1217

#1 A=matrix(3,4,[3,-5,-2,7,2,3,-2,5,9,-3,3,-4]) B=matrix(3,4,[2,-3,4,5,1,7,-9,3,4,5,-4,5]) print(3*A) print(2*A+3*B) print(5*A-2*B) 
        
[  9 -15  -6  21]
[  6   9  -6  15]
[ 27  -9   9 -12]
[ 12 -19   8  29]
[  7  27 -31  19]
[ 30   9  -6   7]
[ 11 -19 -18  25]
[  8   1   8  19]
[ 37 -25  23 -30]
[  9 -15  -6  21]
[  6   9  -6  15]
[ 27  -9   9 -12]
[ 12 -19   8  29]
[  7  27 -31  19]
[ 30   9  -6   7]
[ 11 -19 -18  25]
[  8   1   8  19]
[ 37 -25  23 -30]
#2 A=matrix(3,4,[3,-5,-2,7,2,3,-2,5,9,-3,3,-3]) B=matrix(4,5,[2,-3,4,5,-1,1,7,-9,3,3,4,5,-4,5,-2,3,2,1,-5,7]) print(A*B) 
        
[ 14 -40  72 -45  35]
[ 14  15  -6 -16  46]
[ 18 -39  48  66 -45]
[ 14 -40  72 -45  35]
[ 14  15  -6 -16  46]
[ 18 -39  48  66 -45]
#3 A=matrix(3,3,[8,-5,-7,9,1,-2,5,-3,6]) print(A^0) print(A^2) print(A^3) print((A^2)^4) print(A^8) 
        
[1 0 0]
[0 1 0]
[0 0 1]
[-16 -24 -88]
[ 71 -38 -77]
[ 43 -46   7]
[-784  320 -368]
[-159 -162 -883]
[ -35 -282 -167]
[-20452976  -9380640 -34955184]
[ 28036983 -28932590 -30789429]
[ 17002395 -18304566 -11127905]
[-20452976  -9380640 -34955184]
[ 28036983 -28932590 -30789429]
[ 17002395 -18304566 -11127905]
[1 0 0]
[0 1 0]
[0 0 1]
[-16 -24 -88]
[ 71 -38 -77]
[ 43 -46   7]
[-784  320 -368]
[-159 -162 -883]
[ -35 -282 -167]
[-20452976  -9380640 -34955184]
[ 28036983 -28932590 -30789429]
[ 17002395 -18304566 -11127905]
[-20452976  -9380640 -34955184]
[ 28036983 -28932590 -30789429]
[ 17002395 -18304566 -11127905]
#4 A=matrix(3,4,[1,7,-9,3,4,5,-4,5,3,2,1,-5]) B=matrix(4,5,[1,3,-4,5,-2,2,-3,2,5,-1,5,7,-9,3,3,3,2,1,-5,5]) C=A*B D=A.transpose() F=B.transpose() print bool(C.transpose()==F*D) 
        
True
True
#5 A=matrix(4,4,[3,-5,-2,7,2,3,-2,5,9,-3,3,-4,7,2,4,5]) B=matrix(4,4,[2,-3,4,5,1,7,-9,3,4,5,-4,5,3,2,1,-5]) print bool((A*B).trace()==(B*A).trace()) 
        
True
True
#6 H=diagonal_matrix([5,-1,-2,4,3]) print(H) 
        
[ 5  0  0  0  0]
[ 0 -1  0  0  0]
[ 0  0 -2  0  0]
[ 0  0  0  4  0]
[ 0  0  0  0  3]
[ 5  0  0  0  0]
[ 0 -1  0  0  0]
[ 0  0 -2  0  0]
[ 0  0  0  4  0]
[ 0  0  0  0  3]
#7 A=matrix(3,3,[1,-2,-4,-2,3,-7,-4,-7,6]) B=matrix(3,3,[0,2,-4,-2,0,5,4,-5,0]) I=matrix(3,3,[1,0,0,0,1,0,0,0,1]) print bool(A==A.transpose()) print bool(I==I.transpose()) print bool(B==-B.transpose()) 
        
True
True
True
True
True
True
#12.2 Determinant #1 #a) A=matrix(4,4,[3,-5,-2,4,2,3,-2,-5,5,-3,3,6,1,2,4,-2]) print(A.det()) 
        
-411
-411
#b) A=matrix(4,4,[3,-5,-2,4,2,3,-2,-5,5,-3,3,6,1,2,4,-2]) print((A.transpose()).det()) 
        
-411
-411
#c) A=matrix(4,4,[3,-5,-2,4,2,3,-2,-5,5,-3,3,6,1,2,4,-2]) print(A.adjoint()) 
        
[ -12  -66  -48   -3]
[ 177  -54 -114  147]
[ -29   46   21 -110]
[ 113    5  -96  131]
[ -12  -66  -48   -3]
[ 177  -54 -114  147]
[ -29   46   21 -110]
[ 113    5  -96  131]
#d) A=matrix(4,4,[3,-5,-2,4,2,3,-2,-5,5,-3,3,6,1,2,4,-2]) dA=A.det() print((1/dA)*(A.adjoint())) 
        
[   4/137   22/137   16/137    1/137]
[ -59/137   18/137   38/137  -49/137]
[  29/411  -46/411   -7/137  110/411]
[-113/411   -5/411   32/137 -131/411]
[   4/137   22/137   16/137    1/137]
[ -59/137   18/137   38/137  -49/137]
[  29/411  -46/411   -7/137  110/411]
[-113/411   -5/411   32/137 -131/411]
#2 A=matrix(3,3,[2,-3,4,1,4,-3,3,-2,4]) A1=matrix(3,3,[4,-3,4,8,4,-3,9,-2,4]) A2=matrix(3,3,[2,4,4,1,8,-3,3,9,4]) A3=matrix(3,3,[2,-3,4,1,4,8,3,-2,9]) print('x=',((A1.det())/(A.det()))) print('y=',((A2.det())/(A.det()))) print('z=',((A3.det())/(A.det()))) 
        
('x=', 3)
('y=', 2)
('z=', 1)
('x=', 3)
('y=', 2)
('z=', 1)