UNIDAD 2

224 days ago by claudia.mtz@Tecpabellon

#1 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]
#2 M = MatrixSpace(QQ,4,3) B = M([[6,3,12],[9,5,4],[7,0,5],[11,6,5]]) print "B" print B 
        
B
[ 6  3 12]
[ 9  5  4]
[ 7  0  5]
[11  6  5]
B
[ 6  3 12]
[ 9  5  4]
[ 7  0  5]
[11  6  5]
A*8 
        
[64 32 96]
[80 48 40]
[56 64 40]
[88 56 72]
[64 32 96]
[80 48 40]
[56 64 40]
[88 56 72]
B*8 
        
[48 24 96]
[72 40 32]
[56  0 40]
[88 48 40]
[48 24 96]
[72 40 32]
[56  0 40]
[88 48 40]
A+B 
        
[14  7 24]
[19 11  9]
[14  8 10]
[22 13 14]
[14  7 24]
[19 11  9]
[14  8 10]
[22 13 14]
#3 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]
#4 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]
#5 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]
#6 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]
#7 M = MatrixSpace(QQ,3,4) B = M([[4,1,4,3],[0,-1,3,1],[2,7,5,2]]) print "B" print B 
        
B
[ 4  1  4  3]
[ 0 -1  3  1]
[ 2  7  5  2]
B
[ 4  1  4  3]
[ 0 -1  3  1]
[ 2  7  5  2]
#8 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]
-1*B 
        
[ 0 -2 -7]
[-1  3 -5]
[ 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]
#9 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]
#10 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]
#11 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]
#12 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]
#13 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]
#14 M = MatrixSpace(QQ,2,3) C = M([[1,4,2],[3,1,5]]) print "C" print C 
        
C
[1 4 2]
[3 1 5]
C
[1 4 2]
[3 1 5]
#15 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]
#16 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]
#17 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]
#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]
A*B 
        
[ 8  5]
[20 13]
[ 2  1]
[ 8  5]
[20 13]
[ 2  1]
(A*B)*C 
        
[18 15]
[46 39]
[ 4  3]
[18 15]
[46 39]
[ 4  3]
B*C 
        
[10  9]
[ 4  3]
[10  9]
[ 4  3]
A*(B*C) 
        
[18 15]
[46 39]
[ 4  3]
[18 15]
[46 39]
[ 4  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]
#31 M = MatrixSpace(QQ,4,4) A = M([[5,11,7,3],[2,1,4,-5],[3,-2,8,7],[0,0,0,0]]) print "A" print A 
        
A
[ 5 11  7  3]
[ 2  1  4 -5]
[ 3 -2  8  7]
[ 0  0  0  0]
A
[ 5 11  7  3]
[ 2  1  4 -5]
[ 3 -2  8  7]
[ 0  0  0  0]
#32 M = MatrixSpace(QQ,2,2) A = M([[1,2],[4,5]]) A.inverse() 
        
[-5/3  2/3]
[ 4/3 -1/3]
[-5/3  2/3]
[ 4/3 -1/3]
#33 M = MatrixSpace(QQ,3,3) A = M([[1,2,3],[3,7,6],[1,2,3]]) A.determinant() 
        
0
0
#34 M = MatrixSpace(QQ,3,3) A = M([[3,-1,2],[6,-2,4],[1,7,3]]) A.determinant() 
        
0
0
#35 M = MatrixSpace(QQ,3,3) A = M([[1,2,3],[1,0,1],[1,4,6]]) A.determinant() 
        
-2
-2
#36 M = MatrixSpace(QQ,3,3) A = M([[6,1,1],[-8,4,3],[0,1,3]]) A.determinant() 
        
70
70
M = MatrixSpace(QQ,4,4) A = M([[1,0,0,0],[-9,-1,0,0],[2,7,8,0],[4,5,7,2]]) A.determinant() 
        
-16
-16
#37 M = MatrixSpace(QQ,4,4) A = M(0,3],[2,7,0,6],[0,6,3,0],[7,3,1,-5]]) A.determinant([[1,0,) 
        
-546
-546
#38 M = MatrixSpace(QQ,3,3) A = M([[1,-2,3],[2,7,4],[3,1,4]]) A.determinant() 
        
-41
-41
#39 M = MatrixSpace(QQ,3,3) A = M([[0,1,8],[0,3,3],[4,-1,1]]) A.determinant() 
        
-84
-84
#40 M = MatrixSpace(QQ,3,3) A = M([[-8,12,15],[28,7,35],[4,14,27]]) A.determinant() 
        
476
476
#41 M = MatrixSpace(QQ,2,3) A = M([[10,9,8],[1,2,3]]) B = M([[7,6,5],[4,5,6]]) print "A" print A print "B" print B 
        
A
[10  9  8]
[ 1  2  3]
B
[7 6 5]
[4 5 6]
A
[10  9  8]
[ 1  2  3]
B
[7 6 5]
[4 5 6]
A*B 
        
Traceback (click to the left of this block for traceback)
...
ArithmeticError: self must be a square matrix
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_12.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("QSpC"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpORR1nC/___code___.py", line 2, in <module>
    exec compile(u'A*B
  File "", line 1, in <module>
    
  File "element.pyx", line 2456, in sage.structure.element.Matrix.__mul__ (sage/structure/element.c:16646)
  File "matrix_rational_dense.pyx", line 1027, in sage.matrix.matrix_rational_dense.Matrix_rational_dense._matrix_times_matrix_ (sage/matrix/matrix_rational_dense.c:11585)
  File "matrix_rational_dense.pyx", line 2572, in sage.matrix.matrix_rational_dense.Matrix_rational_dense._multiply_pari (sage/matrix/matrix_rational_dense.c:22743)
ArithmeticError: self must be a square matrix