matrices e inversas

226 days ago by juanhumberto@tecpabellon

#1 M = MatrixSpace(QQ,2,3) A = M([[-1, 2, 4],[ 0, 3, 1]]) B = M([[10, 3, 5],[ 6, 2, 9]]) print "A" print A print "B" print B 
        
A
[-1  2  4]
[ 0  3  1]
B
[10  3  5]
[ 6  2  9]
A
[-1  2  4]
[ 0  3  1]
B
[10  3  5]
[ 6  2  9]
A*5 
        
[-5 10 20]
[ 0 15  5]
[-5 10 20]
[ 0 15  5]
A+B 
        
[ 9  5  9]
[ 6  5 10]
[ 9  5  9]
[ 6  5 10]
#2 M = MatrixSpace(QQ,4,3) A = M([[8, 4, 12],[ 10, 6, 5],[ 7, 8, 5],[ 11, 7, 9]]) B = M([[6, 3, 12],[ 9, 5, 4],[ 7, 0, 5],[11, 6, 5]]) print "A" print A print "B" print B 
        
A
[ 8  4 12]
[10  6  5]
[ 7  8  5]
[11  7  9]
B
[ 6  3 12]
[ 9  5  4]
[ 7  0  5]
[11  6  5]
A
[ 8  4 12]
[10  6  5]
[ 7  8  5]
[11  7  9]
B
[ 6  3 12]
[ 9  5  4]
[ 7  0  5]
[11  6  5]
A*5 
        
[40 20 60]
[50 30 25]
[35 40 25]
[55 35 45]
[40 20 60]
[50 30 25]
[35 40 25]
[55 35 45]
B*5 
        
[30 15 60]
[45 25 20]
[35  0 25]
[55 30 25]
[30 15 60]
[45 25 20]
[35  0 25]
[55 30 25]
#4 M = MatrixSpace(QQ,3,2) C = M([[50, 55],[ 136, 127],[80,79]]) print "C" print C 
        
C
[ 50  55]
[136 127]
[ 80  79]
C
[ 50  55]
[136 127]
[ 80  79]
A*C 
        
[1904 1896]
[1716 1707]
[1838 1796]
[2222 2205]
[1904 1896]
[1716 1707]
[1838 1796]
[2222 2205]
B*C 
        
[1668 1659]
[1450 1446]
[ 750  780]
[1766 1762]
[1668 1659]
[1450 1446]
[ 750  780]
[1766 1762]
#5 E=matrix([[1,1,2],[0,1,-17],[0,3,-11]]) L=E^(-1) print DE print L 
        
[  1   1   2]
[  0   1 -17]
[  0   3 -11]
[     1  17/40 -19/40]
[     0 -11/40  17/40]
[     0  -3/40   1/40]
[  1   1   2]
[  0   1 -17]
[  0   3 -11]
[     1  17/40 -19/40]
[     0 -11/40  17/40]
[     0  -3/40   1/40]
#6 E=matrix([[1,-2,0],[3,4,-1],[2,-1,3]]) L=E^(-1) print DE print L 
        
[  1   1   2]
[  0   1 -17]
[  0   3 -11]
[  1/3  2/11  2/33]
[ -1/3  1/11  1/33]
[ -1/3 -1/11 10/33]
[  1   1   2]
[  0   1 -17]
[  0   3 -11]
[  1/3  2/11  2/33]
[ -1/3  1/11  1/33]
[ -1/3 -1/11 10/33]
#7 E=matrix([[1,1,2],[2,4,-3],[3,6,-5]]) L=E^(-1) print E print L 
        
[ 1  1  2]
[ 2  4 -3]
[ 3  6 -5]
[  2 -17  11]
[ -1  11  -7]
[  0   3  -2]
[ 1  1  2]
[ 2  4 -3]
[ 3  6 -5]
[  2 -17  11]
[ -1  11  -7]
[  0   3  -2]
#8 E=matrix([[1,1,2],[-1,-2,3],[3,-7,4]]) L=E^(-1) print E print L 
        
[ 1  1  2]
[-1 -2  3]
[ 3 -7  4]
[  1/4 -9/26  7/52]
[  1/4 -1/26 -5/52]
[  1/4  5/26 -1/52]
[ 1  1  2]
[-1 -2  3]
[ 3 -7  4]
[  1/4 -9/26  7/52]
[  1/4 -1/26 -5/52]
[  1/4  5/26 -1/52]
#9 E=matrix([[2,1,3],[0,-2,7],[3,4,5]]) L=E^(-1) print E print L 
        
[ 2  1  3]
[ 0 -2  7]
[ 3  4  5]
[ 38/37  -7/37 -13/37]
[-21/37  -1/37  14/37]
[ -6/37   5/37   4/37]
[ 2  1  3]
[ 0 -2  7]
[ 3  4  5]
[ 38/37  -7/37 -13/37]
[-21/37  -1/37  14/37]
[ -6/37   5/37   4/37]
#10 E=matrix([[1,3],[2,7]]) L=E^(-1) print E print L 
        
[1 3]
[2 7]
[ 7 -3]
[-2  1]
[1 3]
[2 7]
[ 7 -3]
[-2  1]
#11 M = MatrixSpace(QQ,3,3) A = M([[3,5, 2],[ 4, 2, 3],[-1,2,4]]) print A 
        
[ 3  5  2]
[ 4  2  3]
[-1  2  4]
[ 3  5  2]
[ 4  2  3]
[-1  2  4]
A.determinant () 
        
-69
-69
#12 M = MatrixSpace(QQ,3,3) A = M([[4,2, 3],[ 3, 5, 2],[-1,2,4]]) print A 
        
[ 4  2  3]
[ 3  5  2]
[-1  2  4]
[ 4  2  3]
[ 3  5  2]
[-1  2  4]
A.determinant () 
        
69
69
#13 M = MatrixSpace(QQ,3,3) A = M([[-1,2,4],[ 3, 5, 2],[4,2,3]]) print A 
        
[-1  2  4]
[ 3  5  2]
[ 4  2  3]
[-1  2  4]
[ 3  5  2]
[ 4  2  3]
A.determinant () 
        
-69
-69
#14 M = MatrixSpace(QQ,3,3) A = M([[1, 0, 4],[ 2, -3, 5],[3,-3,9]]) print A 
        
[ 1  0  4]
[ 2 -3  5]
[ 3 -3  9]
[ 1  0  4]
[ 2 -3  5]
[ 3 -3  9]
A.determinant() 
        
0
0
#15 M = MatrixSpace(QQ,4,3) A = M([[8,4,12],[10,6,5],[7,8,5],[11,7,9]]) print "A" print A 
        
A
[ 8  4 12]
[10  6  5]
[ 7  8  5]
[11  7  9]
A
[ 8  4 12]
[10  6  5]
[ 7  8  5]
[11  7  9]
#16 M = MatrixSpace(QQ,2,2) A = M([[-2,3],[3,-5]]) A.inverse() 
        
[-5 -3]
[-3 -2]
[-5 -3]
[-3 -2]
#17 M = MatrixSpace(QQ,3,3) E = M([[6,1,3],[-1,1,2],[4,1,3]]) A.echelon_form () 
        
[1 0]
[0 1]
[1 0]
[0 1]
#18 M = MatrixSpace(QQ,2,2) A = M([[-1,0],[2,3]]) B = M([[1,2],[3,0]]) print "A" print A print "B" print B 
        
A
[-1  0]
[ 2  3]
B
[1 2]
[3 0]
A
[-1  0]
[ 2  3]
B
[1 2]
[3 0]
#19 M = MatrixSpace(QQ,3,2) A = M([[1,2],[3,4],[0,1]]) print "A" print A 
        
A
[1 2]
[3 4]
[0 1]
A
[1 2]
[3 4]
[0 1]
#20 M = MatrixSpace(QQ,2,2) B = M([[4,3],[2,1]]) C = M([[1,0],[2,3]]) print "B" print B print "C" print C 
        
B
[4 3]
[2 1]
C
[1 0]
[2 3]
B
[4 3]
[2 1]
C
[1 0]
[2 3]
#21 M = MatrixSpace(QQ,3,3) A = M([[1,2,3],[2,5,3],[1,0,8]]) A.echelon_form () 
        
[1 0 0]
[0 1 0]
[0 0 1]
[1 0 0]
[0 1 0]
[0 0 1]
#22 M = MatrixSpace(QQ,2,2) A = M([[1,2],[3,5]]) A.inverse() 
        
[-5  2]
[ 3 -1]
[-5  2]
[ 3 -1]
#23 M = MatrixSpace(QQ,2,2) A = M([[-2,3],[3,-5]]) A.inverse() 
        
[-5 -3]
[-3 -2]
[-5 -3]
[-3 -2]
#24 M = MatrixSpace(QQ,2,2) A = M([[8,-6],[-4,3]]) print "A" print A 
        
A
[ 8 -6]
[-4  3]
A
[ 8 -6]
[-4  3]
#25 M = MatrixSpace(QQ,3,3) A = M([[3,4,-1],[1,0,3],[2,5,-4]]) A.inverse() 
        
[   3/2 -11/10   -6/5]
[    -1      1      1]
[  -1/2   7/10    2/5]
[   3/2 -11/10   -6/5]
[    -1      1      1]
[  -1/2   7/10    2/5]
#26 M = MatrixSpace(QQ,3,3) A = M([[3,1,5],[2,4,1],[-4,2,-9]]) print "A" print A 
        
A
[ 3  1  5]
[ 2  4  1]
[-4  2 -9]
A
[ 3  1  5]
[ 2  4  1]
[-4  2 -9]
#27 M = MatrixSpace(QQ,3,3) A = M([[1,0,1],[0,1,1],[1,1,0]]) A.inverse() 
        
[ 1/2 -1/2  1/2]
[-1/2  1/2  1/2]
[ 1/2  1/2 -1/2]
[ 1/2 -1/2  1/2]
[-1/2  1/2  1/2]
[ 1/2  1/2 -1/2]
#28 M =MatrixSpace(QQ,3,3) A = M([[2,6,6],[2,7,6],[2,7,7]]) A.inverse() 
        
[7/2   0  -3]
[ -1   1   0]
[  0  -1   1]
[7/2   0  -3]
[ -1   1   0]
[  0  -1   1]
#29 M = MatrixSpace(QQ,3,3) A = M([[1/5,1/5,1/5],[1/5,1/5,-4/5],[-2/5,1/10,1/10]]) A.inverse() 
        
[ 1  0 -2]
[ 3  1  2]
[ 1 -1  0]
[ 1  0 -2]
[ 3  1  2]
[ 1 -1  0]
#30 M = MatrixSpace(QQ,4,4) A = M([[1,0,0,0],[1,2,0,0],[1,2,4,0],[1,2,4,8]]) A.inverse() 
        
[   1    0    0    0]
[-1/2  1/2    0    0]
[   0 -1/4  1/4    0]
[   0    0 -1/8  1/8]
[   1    0    0    0]
[-1/2  1/2    0    0]
[   0 -1/4  1/4    0]
[   0    0 -1/8  1/8]
M = MatrixSpace(QQ,4,4) A = M([[1,3,-2,4],[2,6,-4,8],[3,9,1,5],[1,1,4,8]]) A.determinant() 
        
0
0
M = MatrixSpace(QQ,3,3) A = M([[2,-40,17],[0,1,11],[0,0,3]]) A.determinant() 
        
6
6
M = MatrixSpace(QQ,3,3) A = M([[1,2,3],[3,7,6],[1,2,3]]) A.determinant() 
        
0
0