problemas U2

224 days ago by yoya.pedroza@Tecpabellon

#1 M = MatrixSpace(QQ,3,3) A = M([[3,-1,2],[6,-2,4],[1,7,3]]) A.determinant() 
        
0
0
#2 M = MatrixSpace(QQ,2,2) A = M([[1,2],[6,5]]) A.inverse() 
        
[-5/7  2/7]
[ 6/7 -1/7]
[-5/7  2/7]
[ 6/7 -1/7]
#3 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]
#4 M = MatrixSpace(QQ,3,3) A = M([[6,4,5],[5,1,-4],[-2,10,9]]) A.inverse() 
        
[   7/58    1/29   -3/58]
[-37/406  32/203    7/58]
[ 26/203 -34/203   -1/29]
[   7/58    1/29   -3/58]
[-37/406  32/203    7/58]
[ 26/203 -34/203   -1/29]
#5 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]
#6 M = MatrixSpace(QQ,4,4) A = M([[5,11,8,3],[2,1,4,-5],[3,-3,8,7],[0,0,0,0]]) print "A" print A 
        
A
[ 5 11  8  3]
[ 2  1  4 -5]
[ 3 -3  8  7]
[ 0  0  0  0]
A
[ 5 11  8  3]
[ 2  1  4 -5]
[ 3 -3  8  7]
[ 0  0  0  0]
#7 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]
#8 M = MatrixSpace(QQ,3,2) A = M([[1,2],[3,0],[-1,4]]) print "A" print A 
        
A
[ 1  2]
[ 3  0]
[-1  4]
A
[ 1  2]
[ 3  0]
[-1  4]
#9 M = MatrixSpace(QQ,2,3) B = M([[2,1,7],[3,4,2]]) print "B" print B 
        
B
[2 1 7]
[3 4 2]
B
[2 1 7]
[3 4 2]
A*2 
        
[ 2  4]
[ 6  0]
[-2  8]
[ 2  4]
[ 6  0]
[-2  8]
B*2 
        
[ 4  2 14]
[ 6  8  4]
[ 4  2 14]
[ 6  8  4]
#10 M = MatrixSpace(QQ,2,2) A = M([[2,1],[3,4]]) B = M([[2,1],[3,5]]) print "A" print A print "B" print B 
        
A
[2 1]
[3 4]
B
[2 1]
[3 5]
A
[2 1]
[3 4]
B
[2 1]
[3 5]
A*B 
        
[ 7  7]
[18 23]
[ 7  7]
[18 23]
A+B 
        
[4 2]
[6 9]
[4 2]
[6 9]
#11 M = MatrixSpace(QQ,3,4) A = M([[2,1,0,3],[-1,0,2,4],[4,-2,7,0]]) B = M([[-4,3,5,1],[2,2,0,-1],[3,2,-4,5]]) print "A" print A print "B" print B 
        
A
[ 2  1  0  3]
[-1  0  2  4]
[ 4 -2  7  0]
B
[-4  3  5  1]
[ 2  2  0 -1]
[ 3  2 -4  5]
A
[ 2  1  0  3]
[-1  0  2  4]
[ 4 -2  7  0]
B
[-4  3  5  1]
[ 2  2  0 -1]
[ 3  2 -4  5]
A+B 
        
[-2  4  5  4]
[ 1  2  2  3]
[ 7  0  3  5]
[-2  4  5  4]
[ 1  2  2  3]
[ 7  0  3  5]
A-B 
        
[ 6 -2 -5  2]
[-3 -2  2  5]
[ 1 -4 11 -5]
[ 6 -2 -5  2]
[-3 -2  2  5]
[ 1 -4 11 -5]
#11 M = MatrixSpace(QQ,2,3) A = M([[2,3,4],[1,2,1]]) B = M([[0,2,7],[1,-3,5]]) print "A" print A print "B" print B 
        
A
[2 3 4]
[1 2 1]
B
[ 0  2  7]
[ 1 -3  5]
A
[2 3 4]
[1 2 1]
B
[ 0  2  7]
[ 1 -3  5]
A-B 
        
[ 2  1 -3]
[ 0  5 -4]
[ 2  1 -3]
[ 0  5 -4]
A+B 
        
[ 2  5 11]
[ 2 -1  6]
[ 2  5 11]
[ 2 -1  6]
#12 M = MatrixSpace(QQ,2,3) A = M([[1,2,9],[2,10,5]]) print "A" print A 
        
A
[ 1  2  9]
[ 2 10  5]
A
[ 1  2  9]
[ 2 10  5]
#13 M = MatrixSpace(QQ,3,4) B = M([[4,2,4,3],[0,-1,6,1],[2,5,7,2]]) print "B" print B 
        
B
[ 4  2  4  3]
[ 0 -1  6  1]
[ 2  5  7  2]
B
[ 4  2  4  3]
[ 0 -1  6  1]
[ 2  5  7  2]
A*B 
        
[ 22  45  79  23]
[ 18  19 103  26]
[ 22  45  79  23]
[ 18  19 103  26]
#14 M = MatrixSpace(QQ,3,2) A = M([[3,-1,1],[0,2,1]]) print "A" print A 
        
A
[ 3 -1]
[ 1  0]
[ 2  1]
A
[ 3 -1]
[ 1  0]
[ 2  1]
#15 M = MatrixSpace(QQ,2,2) B = M([[4,-1],[0,2]]) A.echelon_form () 
        
[1 0]
[0 1]
[0 0]
[1 0]
[0 1]
[0 0]
#16 M = MatrixSpace(QQ,2,3) A = M([[1,2,3],[4,5,6]]) A.echelon_form () 
        
[ 1  0 -1]
[ 0  1  2]
[ 1  0 -1]
[ 0  1  2]
#17 M = MatrixSpace(QQ,3,4) A = M([[-2,1,-1,4],[1,2,3,13],[3,0,1,-1]]) A.echelon_form () 
        
[ 1  0  0 -1]
[ 0  1  0  4]
[ 0  0  1  2]
[ 1  0  0 -1]
[ 0  1  0  4]
[ 0  0  1  2]
#18 M = MatrixSpace(QQ,3,4) A = M([[1,-2,3,-2],[-1,1,-2,3],[2,-1,3,1]]) A.echelon_form () 
        
[ 1  0  1  0]
[ 0  1 -1  0]
[ 0  0  0  1]
[ 1  0  1  0]
[ 0  1 -1  0]
[ 0  0  0  1]
#19 M = MatrixSpace(QQ,2,3) C = M([[1,6,2],[3,1,7]]) print "C" print C 
        
C
[1 6 2]
[3 1 7]
C
[1 6 2]
[3 1 7]
#20 M = MatrixSpace(QQ,2,3) C = M([[1,8,2],[3,1,9]]) print "C" print C 
        
C
[1 8 2]
[3 1 9]
C
[1 8 2]
[3 1 9]
#21 M = MatrixSpace(QQ,3,3) D = M([[1,5,2],[-1,0,1],[3,2,4]]) A.echelon_form () 
        
[ 1  0  1  0]
[ 0  1 -1  0]
[ 0  0  0  1]
[ 1  0  1  0]
[ 0  1 -1  0]
[ 0  0  0  1]
#22 M = MatrixSpace(QQ,3,3) E = M([[6,1,3],[-1,1,2],[4,1,3]]) A.echelon_form () 
        
[ 1  0  1  0]
[ 0  1 -1  0]
[ 0  0  0  1]
[ 1  0  1  0]
[ 0  1 -1  0]
[ 0  0  0  1]
#23 M = MatrixSpace(QQ,3,3) E = M([[9,1,3],[-1,1,5],[4,10,3]]) A.echelon_form () 
        
[ 1  0  1  0]
[ 0  1 -1  0]
[ 0  0  0  1]
[ 1  0  1  0]
[ 0  1 -1  0]
[ 0  0  0  1]
#24 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]
A*B 
        
[-1 -2]
[11  4]
[-1 -2]
[11  4]
B*A 
        
[ 3  6]
[-3  0]
[ 3  6]
[-3  0]
#25 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]
#26 M = MatrixSpace(QQ,2,2) B = M([[6,2],[2,1]]) C = M([[1,0],[2,5]]) print "B" print B print "C" print C 
        
B
[6 2]
[2 1]
C
[1 0]
[2 5]
B
[6 2]
[2 1]
C
[1 0]
[2 5]
A*B 
        
[10  4]
[26 10]
[ 2  1]
[10  4]
[26 10]
[ 2  1]
(A*B)*C 
        
[18 20]
[46 50]
[ 4  5]
[18 20]
[46 50]
[ 4  5]
B*C 
        
[10 10]
[ 4  5]
[10 10]
[ 4  5]
A*(B*C) 
        
[18 20]
[46 50]
[ 4  5]
[18 20]
[46 50]
[ 4  5]
#27 M = MatrixSpace(QQ,3,3) A = M([[1,4,3],[2,5,3],[1,3,8]]) A.echelon_form () 
        
[1 0 0]
[0 1 0]
[0 0 1]
[1 0 0]
[0 1 0]
[0 0 1]
#28 M = MatrixSpace(QQ,2,2) A = M([[1,2],[3,5]]) A.inverse() 
        
[-5  2]
[ 3 -1]
[-5  2]
[ 3 -1]
#29 M = MatrixSpace(QQ,2,2) A = M([[-2,3],[3,-5]]) A.inverse() 
        
[-5 -3]
[-3 -2]
[-5 -3]
[-3 -2]
#30 M = MatrixSpace(QQ,2,2) A = M([[-5,3],[2,-6]]) A.inverse() 
        
[ -1/4  -1/8]
[-1/12 -5/24]
[ -1/4  -1/8]
[-1/12 -5/24]
#31 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]
#32 M = MatrixSpace(QQ,3,3) A = M([[3,4,-2],[1,0,4],[2,5,-4]]) A.inverse() 
        
[10/11 -3/11 -8/11]
[-6/11  4/11  7/11]
[-5/22  7/22  2/11]
[10/11 -3/11 -8/11]
[-6/11  4/11  7/11]
[-5/22  7/22  2/11]
#33 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]
#34 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]
#35 M = MatrixSpace(QQ,3,3) A = M([[3,7,5],[2,6,1],[4,8,9]]) print "A" print A 
        
A
[3 7 5]
[2 6 1]
[4 8 9]
A
[3 7 5]
[2 6 1]
[4 8 9]
#36 M = MatrixSpace(QQ,4,3) B = M([[6,8,12],[7,5,4],[7,0,5],[11,6,4]]) print "B" print B 
        
B
[ 6  8 12]
[ 7  5  4]
[ 7  0  5]
[11  6  4]
B
[ 6  8 12]
[ 7  5  4]
[ 7  0  5]
[11  6  4]
A*8 
        
[24 56 40]
[16 48  8]
[32 64 72]
[24 56 40]
[16 48  8]
[32 64 72]
B*8 
        
[48 64 96]
[56 40 32]
[56  0 40]
[88 48 32]
[48 64 96]
[56 40 32]
[56  0 40]
[88 48 32]
#37 M = MatrixSpace(QQ,3,4) A = M([[1,6,3,1],[-6,1,-2,3],[8,-1,2,1]]) A.echelon_form () 
        
[     1      0      0      2]
[     0      1      0  43/15]
[     0      0      1 -91/15]
[     1      0      0      2]
[     0      1      0  43/15]
[     0      0      1 -91/15]
#38 M = MatrixSpace(QQ,3,4) A = M([[5,-4,3,-5],[-7,1,-2,4],[1,7,2,4]]) A.echelon_form () 
        
[     1      0      0 -28/59]
[     0      1      0  38/59]
[     0      0      1  -1/59]
[     1      0      0 -28/59]
[     0      1      0  38/59]
[     0      0      1  -1/59]
#39 M = MatrixSpace(QQ,2,3) A = M([[4,5,8],[1,5,3]]) A.echelon_form () 
        
[   1    0  5/3]
[   0    1 4/15]
[   1    0  5/3]
[   0    1 4/15]
#40 M = MatrixSpace(QQ,2,3) A = M([[5,-2,3],[2,-1,3]]) A.echelon_form () 
        
[ 1  0 -3]
[ 0  1 -9]
[ 1  0 -3]
[ 0  1 -9]