unidad2 matrices/Nassira

225 days ago by nazzis666

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]
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]
M = MatrixSpace(QQ,2,2) B = M([[4,-1],[0,2]]) A.echelon_form () 
        
[ 1  0 -1]
[ 0  1  2]
[ 1  0 -1]
[ 0  1  2]
M = MatrixSpace(QQ,3,2) A = M([[1,2],[3,4],[0,1]]) print "A" print A 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 
        
A
[1 2]
[3 4]
[0 1]
B
[4 3]
[2 1]
C
[1 0]
[2 3]
A
[1 2]
[3 4]
[0 1]
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]
M = MatrixSpace(QQ,3,2) A = M([[1,2],[3,0],[-1,4]]) print "A" print A M = MatrixSpace(QQ,2,3) B = M([[2,1,7],[3,4,2]]) print "B" print B 
        
A
[ 1  2]
[ 3  0]
[-1  4]
B
[2 1 7]
[3 4 2]
A
[ 1  2]
[ 3  0]
[-1  4]
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]
M = MatrixSpace(QQ,4,3) A = M([[8,4,12],[10,6,5],[7,8,5],[11,7,9]]) print "A" print A M = MatrixSpace(QQ,4,3) B = M([[6,3,12],[9,5,4],[7,0,5],[11,6,5]]) 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*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]
M = MatrixSpace(QQ,3,2) A = M([[1,2],[3,4],[0,1]]) print "A" print A 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 
        
A
[1 2]
[3 4]
[0 1]
B
[4 3]
[2 1]
C
[1 0]
[2 3]
A
[1 2]
[3 4]
[0 1]
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]
 
       
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*2 
        
[4 2]
[6 8]
[4 2]
[6 8]
B*2 
        
[ 4  2]
[ 6 10]
[ 4  2]
[ 6 10]
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]
M = MatrixSpace(QQ,3,2) A = M([[1,2],[3,0],[-1,4]]) print "A" print A M = MatrixSpace(QQ,2,3) B = M([[2,1,7],[3,4,2]]) print "B" print B 
        
A
[ 1  2]
[ 3  0]
[-1  4]
B
[2 1 7]
[3 4 2]
A
[ 1  2]
[ 3  0]
[-1  4]
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]
A+B 
        
Traceback (click to the left of this block for traceback)
...
TypeError: unsupported operand parent(s) for '+': 'Full MatrixSpace of 3
by 2 dense matrices over Rational Field' and 'Full MatrixSpace of 2 by 3
dense matrices over Rational Field'
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_37.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("QStC"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmp5OjU2z/___code___.py", line 2, in <module>
    exec compile(u'A+B
  File "", line 1, in <module>
    
  File "element.pyx", line 1297, in sage.structure.element.RingElement.__add__ (sage/structure/element.c:11458)
  File "coerce.pyx", line 766, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:7337)
TypeError: unsupported operand parent(s) for '+': 'Full MatrixSpace of 3 by 2 dense matrices over Rational Field' and 'Full MatrixSpace of 2 by 3 dense matrices over Rational Field'
M = MatrixSpace(QQ,2,3) A = M([[1,2,4],[2,6,0]]) print "A" print A M = MatrixSpace(QQ,3,4) B = M([[4,1,4,3],[0,-1,3,1],[2,7,5,2]]) print "B" print B 
        
A
[1 2 4]
[2 6 0]
B
[ 4  1  4  3]
[ 0 -1  3  1]
[ 2  7  5  2]
A
[1 2 4]
[2 6 0]
B
[ 4  1  4  3]
[ 0 -1  3  1]
[ 2  7  5  2]
A*B 
        
[12 27 30 13]
[ 8 -4 26 12]
[12 27 30 13]
[ 8 -4 26 12]
M = MatrixSpace(QQ,2,2) A = M([[3,6],[3,7]]) B = M([[5,1],[5,5]]) print "A" print A print "B" print B 
        
A
[3 6]
[3 7]
B
[5 1]
[5 5]
A
[3 6]
[3 7]
B
[5 1]
[5 5]
A*B 
        
[45 33]
[50 38]
[45 33]
[50 38]
A+B 
        
[ 8  7]
[ 8 12]
[ 8  7]
[ 8 12]
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]
M = MatrixSpace(QQ,2,3) A = M([[8,3,4],[1,2,1]]) B = M([[0,3,7],[1,-3,5]]) print "A" print A print "B" print B 
        
A
[8 3 4]
[1 2 1]
B
[ 0  3  7]
[ 1 -3  5]
A
[8 3 4]
[1 2 1]
B
[ 0  3  7]
[ 1 -3  5]
-1*B 
        
[ 0 -3 -7]
[-1  3 -5]
[ 0 -3 -7]
[-1  3 -5]
A+B 
        
[ 8  6 11]
[ 2 -1  6]
[ 8  6 11]
[ 2 -1  6]
A-B 
        
[ 8  0 -3]
[ 0  5 -4]
[ 8  0 -3]
[ 0  5 -4]
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]
M = MatrixSpace(QQ,2,3) A = M([[3,2,3],[6,3,0]]) print "A" print A M = MatrixSpace(QQ,3,4) B = M([[7,1,1,3],[0,-2,6,1],[2,7,2,2]]) print "B" print B 
        
A
[3 2 3]
[6 3 0]
B
[ 7  1  1  3]
[ 0 -2  6  1]
[ 2  7  2  2]
A
[3 2 3]
[6 3 0]
B
[ 7  1  1  3]
[ 0 -2  6  1]
[ 2  7  2  2]
A*B 
        
[27 20 21 17]
[42  0 24 21]
[27 20 21 17]
[42  0 24 21]
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]
M = MatrixSpace(QQ,2,2) A = M([[-2,0],[2,4]]) B = M([[3,2],[4,0]]) print "A" print A print "B" print B 
        
A
[-2  0]
[ 2  4]
B
[3 2]
[4 0]
A
[-2  0]
[ 2  4]
B
[3 2]
[4 0]
A*B 
        
[-6 -4]
[22  4]
[-6 -4]
[22  4]
B*A 
        
[-2  8]
[-8  0]
[-2  8]
[-8  0]
M = MatrixSpace(QQ,2,2) B = M([[6,-1],[0,3]]) A.echelon_form () 
        
[1 0]
[0 1]
[1 0]
[0 1]
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]
M = MatrixSpace(QQ,2,2) A = M([[-2,3],[3,-5]]) A.inverse() 
        
[-5 -3]
[-3 -2]
[-5 -3]
[-3 -2]
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]
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]
M = MatrixSpace(QQ,2,3) C = M([[5,4,2],[4,1,5]]) print "C" print C 
        
C
[5 4 2]
[4 1 5]
C
[5 4 2]
[4 1 5]
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]
M = MatrixSpace(QQ,3,3) E = M([[6,1,3],[-1,1,2],[4,1,3]]) A.echelon_form () 
        
[1 0 0]
[0 1 0]
[0 0 1]
[1 0 0]
[0 1 0]
[0 0 1]
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]
M = MatrixSpace(QQ,2,2) A = M([[1,2],[3,5]]) A.inverse() 
        
[-5  2]
[ 3 -1]
[-5  2]
[ 3 -1]
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]
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([[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]
M = MatrixSpace(QQ,2,2) A = M([[1,2],[2,2]]) A.inverse() 
        
[  -1    1]
[   1 -1/2]
[  -1    1]
[   1 -1/2]
M = MatrixSpace(QQ,2,2) A = M([[-4,-2],[5,5]]) A.inverse() 
        
[-1/2 -1/5]
[ 1/2  2/5]
[-1/2 -1/5]
[ 1/2  2/5]
M = MatrixSpace(QQ,3,3) A = M([[10,12,6],[2,5/2,3/2],[2,2,3/2]]) A.inverse() 
        
[ 1/2   -4    2]
[   0    2   -2]
[-2/3  8/3  2/3]
[ 1/2   -4    2]
[   0    2   -2]
[-2/3  8/3  2/3]
M = MatrixSpace(QQ,3,7) A = M([[16,16,5,15,5,20,20],[18,1,27,27,7,9,5],[5,18,20,14,15,1,27]]) print "A" print A M = MatrixSpace(QQ,3,3) B= M([[-3,-3,-4],[0,1,1],[4,3,0]]) print "B" print B 
        
A
[16 16  5 15  5 20 20]
[18  1 27 27  7  9  5]
[ 5 18 20 14 15  1 27]
B
[-3 -3 -4]
[ 0  1  1]
[ 4  3  0]
A
[16 16  5 15  5 20 20]
[18  1 27 27  7  9  5]
[ 5 18 20 14 15  1 27]
B
[-3 -3 -4]
[ 0  1  1]
[ 4  3  0]
B*A 
        
[-122 -123 -176 -182  -96  -91 -183]
[  23   19   47   41   22   10   32]
[ 118   67  101  141   41  107   95]
[-122 -123 -176 -182  -96  -91 -183]
[  23   19   47   41   22   10   32]
[ 118   67  101  141   41  107   95]
B.inverse() 
        
[ -3/13 -12/13   1/13]
[  4/13  16/13   3/13]
[ -4/13  -3/13  -3/13]
[ -3/13 -12/13   1/13]
[  4/13  16/13   3/13]
[ -4/13  -3/13  -3/13]
M = MatrixSpace(QQ,3,7) A = M([[-122,-123,-176,-182,-96,-91,-183],[23,19,47,41,22,10,32],[118,67,101,141,41,107,95]]) print "A" print A M = MatrixSpace(QQ,3,3) B = M([[-3/13,-12/13,1/13],[4/13,16/13,3/13],[-4/13,-3/13,-3/13]]) print "B" print B 
        
A
[-122 -123 -176 -182  -96  -91 -183]
[  23   19   47   41   22   10   32]
[ 118   67  101  141   41  107   95]
B
[ -3/13 -12/13   1/13]
[  4/13  16/13   3/13]
[ -4/13  -3/13  -3/13]
A
[-122 -123 -176 -182  -96  -91 -183]
[  23   19   47   41   22   10   32]
[ 118   67  101  141   41  107   95]
B
[ -3/13 -12/13   1/13]
[  4/13  16/13   3/13]
[ -4/13  -3/13  -3/13]
B*A 
        
[16 16  5 15  5 20 20]
[18  1 27 27  7  9  5]
[ 5 18 20 14 15  1 27]
[16 16  5 15  5 20 20]
[18  1 27 27  7  9  5]
[ 5 18 20 14 15  1 27]
M = MatrixSpace(QQ,3,6) A = M([[139,47,140,97,86,132],[36,9,32,23,19,39],[56,47,66,51,49,31]]) print "A" print A 
        
A
[139  47 140  97  86 132]
[ 36   9  32  23  19  39]
[ 56  47  66  51  49  31]
A
[139  47 140  97  86 132]
[ 36   9  32  23  19  39]
[ 56  47  66  51  49  31]
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) B = M([[-1,3,1],[-1,7/2,1/2],[1,-5/2,-1/2]]) B.determinant() 
        
-1/2
-1/2
M = MatrixSpace(QQ,4,4) A = M([[1,0,0,3],[2,7,0,6],[0,6,3,0],[7,3,1,-5]]) A.determinant() 
        
-546
-546