MATRICES KARINA

224 days ago by karina.almendaris@tecpabellon

#1 A=matrix([[-2,1,-1,4],[1,2,3,13],[3,0,1,-1]]) print A 
        
[-2  1 -1  4]
[ 1  2  3 13]
[ 3  0  1 -1]
[-2  1 -1  4]
[ 1  2  3 13]
[ 3  0  1 -1]
#2 A=matrix([[-2,1,-1,],[1,2,3,],[3,0,1,]]) A.inverse() 
        
[  1/5 -1/10   1/2]
[  4/5  1/10   1/2]
[ -3/5  3/10  -1/2]
[  1/5 -1/10   1/2]
[  4/5  1/10   1/2]
[ -3/5  3/10  -1/2]
#3 A = Matrix([[9, 8],[ 5,7],[6,4]]) B = Matrix([[540,630,530],[ 420,410,440]]) print "A" print A print "B" print B 
        
A
[9 8]
[5 7]
[6 4]
B
[540 630 530]
[420 410 440]
A
[9 8]
[5 7]
[6 4]
B
[540 630 530]
[420 410 440]
A*B 
        
[8220 8950 8290]
[5640 6020 5730]
[4920 5420 4940]
[8220 8950 8290]
[5640 6020 5730]
[4920 5420 4940]
#4 A=matrix([[1,2,3],[4,5,6]]) A 
        
[1 2 3]
[4 5 6]
[1 2 3]
[4 5 6]
A.echelon () 
        
Traceback (click to the left of this block for traceback)
...
AttributeError: 'sage.matrix.matrix_integer_dense.Matrix_integer_dense'
object has no attribute 'echelon'
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_35.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("QS5lY2hlbG9uICgp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpNWIUlM/___code___.py", line 2, in <module>
    exec compile(u'A.echelon ()
  File "", line 1, in <module>
    
  File "element.pyx", line 328, in sage.structure.element.Element.__getattr__ (sage/structure/element.c:2790)
  File "parent.pyx", line 277, in sage.structure.parent.getattr_from_other_class (sage/structure/parent.c:2930)
  File "parent.pyx", line 175, in sage.structure.parent.raise_attribute_error (sage/structure/parent.c:2699)
AttributeError: 'sage.matrix.matrix_integer_dense.Matrix_integer_dense' object has no attribute 'echelon'
#5 A=matrix([[-2,1,-1],[1,2,3],[3,0,1,]]) print A 
        
[-2  1 -1]
[ 1  2  3]
[ 3  0  1]
[-2  1 -1]
[ 1  2  3]
[ 3  0  1]
A.inverse() 
        
[  1/5 -1/10   1/2]
[  4/5  1/10   1/2]
[ -3/5  3/10  -1/2]
[  1/5 -1/10   1/2]
[  4/5  1/10   1/2]
[ -3/5  3/10  -1/2]
#6 A=matrix([[1,-2,-3,],[-1,1,-2,],[2,-1,3,]]) print A 
        
[ 1 -2 -3]
[-1  1 -2]
[ 2 -1  3]
[ 1 -2 -3]
[-1  1 -2]
[ 2 -1  3]
A.inverse() 
        
[ 1/6  3/2  7/6]
[-1/6  3/2  5/6]
[-1/6 -1/2 -1/6]
[ 1/6  3/2  7/6]
[-1/6  3/2  5/6]
[-1/6 -1/2 -1/6]
#7 A=matrix([[1,2,],[4,5]]) print A 
        
[1 2]
[4 5]
[1 2]
[4 5]
A.inverse() 
        
[-5/3  2/3]
[ 4/3 -1/3]
[-5/3  2/3]
[ 4/3 -1/3]
#8 A=matrix([[1,2,3],[2,5,3],[1,0,8]]) print A 
        
[1 2 3]
[2 5 3]
[1 0 8]
[1 2 3]
[2 5 3]
[1 0 8]
A.inverse() 
        
[-40  16   9]
[ 13  -5  -3]
[  5  -2  -1]
[-40  16   9]
[ 13  -5  -3]
[  5  -2  -1]
#9 A=matrix([[-4,-2,],[5,5]]) print A 
        
[-4 -2]
[ 5  5]
[-4 -2]
[ 5  5]
A.inverse() 
        
[-1/2 -1/5]
[ 1/2  2/5]
[-1/2 -1/5]
[ 1/2  2/5]
#10 A = Matrix([[-3,-3,-4],[ 0,1,1],[4,3,0]]) B = Matrix([[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 print "B" print B 
        
A
[-3 -3 -4]
[ 0  1  1]
[ 4  3  0]
B
[16 16  5 15  5 20 20]
[18  1 27 27  7  9  5]
[ 5 18 20 14 15  1 27]
A
[-3 -3 -4]
[ 0  1  1]
[ 4  3  0]
B
[16 16  5 15  5 20 20]
[18  1 27 27  7  9  5]
[ 5 18 20 14 15  1 27]
A*B 
        
[-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]
#11 A=matrix([[-3,-3,-4],[0,1,1],[4,3,0]]) print A 
        
[-3 -3 -4]
[ 0  1  1]
[ 4  3  0]
[-3 -3 -4]
[ 0  1  1]
[ 4  3  0]
A.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]
#12 A=matrix([[1,1,2],[2,4,-3],[3,6,-5]]) print A 
        
[ 1  1  2]
[ 2  4 -3]
[ 3  6 -5]
[ 1  1  2]
[ 2  4 -3]
[ 3  6 -5]
A.inverse() 
        
[  2 -17  11]
[ -1  11  -7]
[  0   3  -2]
[  2 -17  11]
[ -1  11  -7]
[  0   3  -2]
#13 A=matrix([[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.inverse() 
        
[ -2/69  16/69 -11/69]
[ 19/69 -14/69   1/69]
[-10/69  11/69  14/69]
[ -2/69  16/69 -11/69]
[ 19/69 -14/69   1/69]
[-10/69  11/69  14/69]
#14 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]
#15 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]
#16 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]
#17 M = MatrixSpace(QQ,2,2) A = M([[1,3],[2,2]]) A.inverse() 
        
[-1/2  3/4]
[ 1/2 -1/4]
[-1/2  3/4]
[ 1/2 -1/4]
#18 M = MatrixSpace(QQ,2,2) A = M([[5,-6],[-3,3]]) print "A" print A 
        
A
[ 5 -6]
[-3  3]
A
[ 5 -6]
[-3  3]
#19 M = MatrixSpace(QQ,4,4) A = M([[5,11,7,4],[2,1,4,-3],[3,-1,8,7],[0,0,0,0]]) print "A" print A 
        
A
[ 5 11  7  4]
[ 2  1  4 -3]
[ 3 -1  8  7]
[ 0  0  0  0]
A
[ 5 11  7  4]
[ 2  1  4 -3]
[ 3 -1  8  7]
[ 0  0  0  0]
#20 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]
#21 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]
#22 M = MatrixSpace(QQ,3,3) A = M([[-1,2,4],[4,2,3],[3,5,2]]) A.determinant() 
        
69
69
#23 M = MatrixSpace(QQ,3,3) A = M([[2,-40,16],[0,0,11],[0,0,2]]) A.determinant() 
        
0
0
#24 M = MatrixSpace(QQ,3,3) A = M([[1,2,3,],[3,7,6,],[1,2,3,]]) A.determinant() 
        
0
0
#25 M = MatrixSpace(QQ,2,2) B = M([[4,-2],[0,2]]) A.echelon_form () 
        
[ 1  0  9]
[ 0  1 -3]
[ 0  0  0]
[ 1  0  9]
[ 0  1 -3]
[ 0  0  0]
#26 M = MatrixSpace(QQ,2,2) B = M([[3,-2],[1,2]]) A.echelon_form () 
        
[ 1  0  9]
[ 0  1 -3]
[ 0  0  0]
[ 1  0  9]
[ 0  1 -3]
[ 0  0  0]
#27 M = MatrixSpace(QQ,2,2) A = M([[1,2],[3,5]]) A.inverse() 
        
[-5  2]
[ 3 -1]
[-5  2]
[ 3 -1]
#28 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]
#29 M = MatrixSpace(QQ,3,3) A = M([[1,2,3],[1,7,5],[1,2,3]]) A.determinant() 
        
0
0
#30 M = MatrixSpace(QQ,3,3) A = M([[1,-2,3],[2,7,4],[3,1,4]]) A.determinant() 
        
-41
-41
#31 M = MatrixSpace(QQ,2,2) B = M([[4,-1],[0,2]]) A.echelon_form () 
        
[1 0 0]
[0 1 0]
[0 0 1]
[1 0 0]
[0 1 0]
[0 0 1]
#32 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]
#33 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]
#34 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]
#35 M = MatrixSpace(QQ,2,2) A = M([[7,-5],[-3,2]]) print "A" print A 
        
A
[ 7 -5]
[-3  2]
A
[ 7 -5]
[-3  2]
#36 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]
#37 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]
#38 M = MatrixSpace(QQ,2,2) A = M([[1,1],[3,5]]) A.inverse() 
        
[ 5/2 -1/2]
[-3/2  1/2]
[ 5/2 -1/2]
[-3/2  1/2]
#39 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 
        
B
[ -3/13 -12/13   1/13]
[  4/13  16/13   3/13]
[ -4/13  -3/13  -3/13]
B
[ -3/13 -12/13   1/13]
[  4/13  16/13   3/13]
[ -4/13  -3/13  -3/13]
#40 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]