UNIDAD 2 SAGE

224 days ago by ange.patty@Tecpabellon

#1 A= matrix([[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  4 12]
[10  6  5]
[ 7  8  5]
[11  7  9]
#2 A= matrix([[6,3,12],[9,5,4],[7,0,5],[11,6,5]]) A 
        
[ 6  3 12]
[ 9  5  4]
[ 7  0  5]
[11  6  5]
[ 6  3 12]
[ 9  5  4]
[ 7  0  5]
[11  6  5]
#3 A= matrix([[14,7,24],[19,11,9],[14,8,10],[22,13,14]]) A 
        
[14  7 24]
[19 11  9]
[14  8 10]
[22 13 14]
[14  7 24]
[19 11  9]
[14  8 10]
[22 13 14]
#4 A= matrix([[2,1,0],[1,1,1],[0,8,0],[0,1,4]]) A 
        
[2 1 0]
[1 1 1]
[0 8 0]
[0 1 4]
[2 1 0]
[1 1 1]
[0 8 0]
[0 1 4]
#5 A= matrix([[1,2,3],[4,5,6]]) A 
        
[1 2 3]
[4 5 6]
[1 2 3]
[4 5 6]
A.echelon_form () 
        
[1 2 3]
[0 3 6]
[1 2 3]
[0 3 6]
#6 A= matrix([[-2,1,-1,4],[1,2,3,13],[3,0,1,-1]]) 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]
A.echelon_form () 
        
[ 1  0  7 13]
[ 0  1  3 10]
[ 0  0 10 20]
[ 1  0  7 13]
[ 0  1  3 10]
[ 0  0 10 20]
#7 A= matrix([[1,-2,3,-2],[-1,1,-2,3],[2,-1,3,1]]) A 
        
[ 1 -2  3 -2]
[-1  1 -2  3]
[ 2 -1  3  1]
[ 1 -2  3 -2]
[-1  1 -2  3]
[ 2 -1  3  1]
A.echelon_form () 
        
[ 1  0  1  4]
[ 0  1 -1  7]
[ 0  0  0  8]
[ 1  0  1  4]
[ 0  1 -1  7]
[ 0  0  0  8]
#8 A= matrix([[1,2],[4,5]]) 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]
#9 A= matrix([[4,3,10],[5,8,1],[6,9,2]]) A 
        
[ 4  3 10]
[ 5  8  1]
[ 6  9  2]
[ 4  3 10]
[ 5  8  1]
[ 6  9  2]
A. echelon_form () 
        
[ 1  0  7]
[ 0  1  8]
[ 0  0 14]
[ 1  0  7]
[ 0  1  8]
[ 0  0 14]
A.inverse () 
        
[  -1/2     -6   11/2]
[   2/7   26/7  -23/7]
[  3/14    9/7 -17/14]
[  -1/2     -6   11/2]
[   2/7   26/7  -23/7]
[  3/14    9/7 -17/14]
#10 A= matrix([[1,1,2,9],[0,2,-7,-17],[0,3,-11,-27]]) A 
        
[  1   1   2   9]
[  0   2  -7 -17]
[  0   3 -11 -27]
[  1   1   2   9]
[  0   2  -7 -17]
[  0   3 -11 -27]
A.echelon_form () 
        
[1 0 0 1]
[0 1 0 2]
[0 0 1 3]
[1 0 0 1]
[0 1 0 2]
[0 0 1 3]
#11 A= matrix([[2,4,-7,0,8],[-3,4,-7,8,5]]) A 
        
[ 2  4 -7  0  8]
[-3  4 -7  8  5]
[ 2  4 -7  0  8]
[-3  4 -7  8  5]
A.echelon_form () 
        
[  1  12 -21   8  21]
[  0  20 -35  16  34]
[  1  12 -21   8  21]
[  0  20 -35  16  34]
#12 A= matrix([[1,-2,0],[3,4,-1],[2,-1,3]]) A 
        
[ 1 -2  0]
[ 3  4 -1]
[ 2 -1  3]
[ 1 -2  0]
[ 3  4 -1]
[ 2 -1  3]
A.echelon_form () 
        
[ 1  0 13]
[ 0  1 23]
[ 0  0 33]
[ 1  0 13]
[ 0  1 23]
[ 0  0 33]
#13 A= matrix([[1,0,1,1],[-1,2,-1,3]]) A 
        
[ 1  0  1  1]
[-1  2 -1  3]
[ 1  0  1  1]
[-1  2 -1  3]
A.echelon_form () 
        
[1 0 1 1]
[0 2 0 4]
[1 0 1 1]
[0 2 0 4]
#14 A= matrix([[1,0,1,1],[-1,2,-1,3]]) A 
        
[ 1  0  1  1]
[-1  2 -1  3]
[ 1  0  1  1]
[-1  2 -1  3]
A.echelon_form () 
        
[1 0 1 1]
[0 2 0 4]
[1 0 1 1]
[0 2 0 4]
#15 A= matrix([[1,0,1,0,0,1],[0,2,-1,0,1,2],[0,0,2,1,0,3]]) A 
        
[ 1  0  1  0  0  1]
[ 0  2 -1  0  1  2]
[ 0  0  2  1  0  3]
[ 1  0  1  0  0  1]
[ 0  2 -1  0  1  2]
[ 0  0  2  1  0  3]
A.echelon_form () 
        
[1 0 1 0 0 1]
[0 2 1 1 1 5]
[0 0 2 1 0 3]
[1 0 1 0 0 1]
[0 2 1 1 1 5]
[0 0 2 1 0 3]
#16 A= matrix([[1,0,1],[1,1,2]]) A 
        
[1 0 1]
[1 1 2]
[1 0 1]
[1 1 2]
A.echelon_form () 
        
[1 0 1]
[0 1 1]
[1 0 1]
[0 1 1]
#17 A= matrix([[1,0,-1,2],[2,1,1,3],[1,-1,2,4]]) A 
        
[ 1  0 -1  2]
[ 2  1  1  3]
[ 1 -1  2  4]
[ 1  0 -1  2]
[ 2  1  1  3]
[ 1 -1  2  4]
A.echelon_form () 
        
[ 1  0  5  3]
[ 0  1  3 -1]
[ 0  0  6  1]
[ 1  0  5  3]
[ 0  1  3 -1]
[ 0  0  6  1]
#18 A= matrix([[1,0,0],[0,1,0],[1,-1,1]]) A 
        
[ 1  0  0]
[ 0  1  0]
[ 1 -1  1]
[ 1  0  0]
[ 0  1  0]
[ 1 -1  1]
A.echelon_form () 
        
[1 0 0]
[0 1 0]
[0 0 1]
[1 0 0]
[0 1 0]
[0 0 1]
#19 A= matrix([[1,2,3,4,5],[5,4,3,2,1]]) A 
        
[1 2 3 4 5]
[5 4 3 2 1]
[1 2 3 4 5]
[5 4 3 2 1]
A.echelon_form () 
        
[ 1  2  3  4  5]
[ 0  6 12 18 24]
[ 1  2  3  4  5]
[ 0  6 12 18 24]
#20 A= matrix([[1,0,0,0,1],[0,1,0,0,2],[0,0,1,0,3],[0,0,0,1,4]]) A 
        
[1 0 0 0 1]
[0 1 0 0 2]
[0 0 1 0 3]
[0 0 0 1 4]
[1 0 0 0 1]
[0 1 0 0 2]
[0 0 1 0 3]
[0 0 0 1 4]
#21 A= matrix([[-2,1,-1,4],[1,2,3,13],[3,0,1,-1]]) 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]
A.echelon_form () 
        
[ 1  0  7 13]
[ 0  1  3 10]
[ 0  0 10 20]
[ 1  0  7 13]
[ 0  1  3 10]
[ 0  0 10 20]
#22 A= matrix([[1,1,2,9],[0,2,-7,-17],[0,3,-11,-27]]) A 
        
[  1   1   2   9]
[  0   2  -7 -17]
[  0   3 -11 -27]
[  1   1   2   9]
[  0   2  -7 -17]
[  0   3 -11 -27]
A.echelon_form () 
        
[1 0 0 1]
[0 1 0 2]
[0 0 1 3]
[1 0 0 1]
[0 1 0 2]
[0 0 1 3]
#23 A= matrix([[1,-2,0],[3,4,-1],[2,-1,3]]) A 
        
[ 1 -2  0]
[ 3  4 -1]
[ 2 -1  3]
[ 1 -2  0]
[ 3  4 -1]
[ 2 -1  3]
A.echelon_form () 
        
[ 1  0 13]
[ 0  1 23]
[ 0  0 33]
[ 1  0 13]
[ 0  1 23]
[ 0  0 33]
#24 A= matrix([[2,2,2,0],[-2,5,2,0],[-7,7,1,0]]) A 
        
[ 2  2  2  0]
[-2  5  2  0]
[-7  7  1  0]
[ 2  2  2  0]
[-2  5  2  0]
[-7  7  1  0]
A.echelon_form() 
        
[1 1 1 0]
[0 7 4 0]
[0 0 0 0]
[1 1 1 0]
[0 7 4 0]
[0 0 0 0]
#25 A= matrix([[1,3,-2,0,2,0,0],[2,6,-5,-2,4,-3,-1],[0,0,5,10,0,15,5],[2,6,0,8,4,18,6]]) A 
        
[ 1  3 -2  0  2  0  0]
[ 2  6 -5 -2  4 -3 -1]
[ 0  0  5 10  0 15  5]
[ 2  6  0  8  4 18  6]
[ 1  3 -2  0  2  0  0]
[ 2  6 -5 -2  4 -3 -1]
[ 0  0  5 10  0 15  5]
[ 2  6  0  8  4 18  6]
A.echelon_form () 
        
[1 3 0 4 2 0 0]
[0 0 1 2 0 3 1]
[0 0 0 0 0 6 2]
[0 0 0 0 0 0 0]
[1 3 0 4 2 0 0]
[0 0 1 2 0 3 1]
[0 0 0 0 0 6 2]
[0 0 0 0 0 0 0]
#26 A= matrix([[1,1,2,9],[2,4,-3,1],[3,6,-5,0]]) A 
        
[ 1  1  2  9]
[ 2  4 -3  1]
[ 3  6 -5  0]
[ 1  1  2  9]
[ 2  4 -3  1]
[ 3  6 -5  0]
A.echelon_form () 
        
[1 0 0 1]
[0 1 0 2]
[0 0 1 3]
[1 0 0 1]
[0 1 0 2]
[0 0 1 3]
#27 M=matrix([[16,16,5,15,5,20,20],[18,1,27,27,7,9,5],[5,18,20,14,15,1,27]]) E=matrix([[-3,-3,-4],[0,1,1],[4,3,0]]) L=E^(-1) EC=E*M print EC DE=E^(-1)*EC print DE print L 
        
[-122 -123 -176 -182  -96  -91 -183]
[  23   19   47   41   22   10   32]
[ 118   67  101  141   41  107   95]
[16 16  5 15  5 20 20]
[18  1 27 27  7  9  5]
[ 5 18 20 14 15  1 27]
[ -3/13 -12/13   1/13]
[  4/13  16/13   3/13]
[ -4/13  -3/13  -3/13]
[-122 -123 -176 -182  -96  -91 -183]
[  23   19   47   41   22   10   32]
[ 118   67  101  141   41  107   95]
[16 16  5 15  5 20 20]
[18  1 27 27  7  9  5]
[ 5 18 20 14 15  1 27]
[ -3/13 -12/13   1/13]
[  4/13  16/13   3/13]
[ -4/13  -3/13  -3/13]
#28 M=matrix([[25,27,22,23,20,16],[15,8,5,9,5,20],[21,1,27,14,14,19]]) E=matrix([[1,2,4],[0,1,1],[2,-1,1]]) L=E^(-1) EC=E*M print EC DE=E^(-1)*EC print DE print L 
        
[139  47 140  97  86 132]
[ 36   9  32  23  19  39]
[ 56  47  66  51  49  31]
[25 27 22 23 20 16]
[15  8  5  9  5 20]
[21  1 27 14 14 19]
[  -1    3    1]
[  -1  7/2  1/2]
[   1 -5/2 -1/2]
[139  47 140  97  86 132]
[ 36   9  32  23  19  39]
[ 56  47  66  51  49  31]
[25 27 22 23 20 16]
[15  8  5  9  5 20]
[21  1 27 14 14 19]
[  -1    3    1]
[  -1  7/2  1/2]
[   1 -5/2 -1/2]
#29 A= matrix([[1,1,-2,8],[-1,-2,3,1],[3,-7,4,10]]) A 
        
[ 1  1 -2  8]
[-1 -2  3  1]
[ 3 -7  4 10]
[ 1  1 -2  8]
[-1 -2  3  1]
[ 3 -7  4 10]
A.echelon_form () 
        
[  1   0  -1  17]
[  0   1  -1  95]
[  0   0   0 104]
[  1   0  -1  17]
[  0   1  -1  95]
[  0   0   0 104]
#30 A= matrix([[2,2,2,0],[-2,5,2,0],[-7,7,1,0]]) A 
        
[ 2  2  2  0]
[-2  5  2  0]
[-7  7  1  0]
[ 2  2  2  0]
[-2  5  2  0]
[-7  7  1  0]
A.echelon_form () 
        
[1 1 1 0]
[0 7 4 0]
[0 0 0 0]
[1 1 1 0]
[0 7 4 0]
[0 0 0 0]
#31 A= matrix([[1,-1,2,-1,-1],[2,1,-2,-2,-2],[-1,2,-4,1,1], [3,0,0,-3,-3]]) A 
        
[ 1 -1  2 -1 -1]
[ 2  1 -2 -2 -2]
[-1  2 -4  1  1]
[ 3  0  0 -3 -3]
[ 1 -1  2 -1 -1]
[ 2  1 -2 -2 -2]
[-1  2 -4  1  1]
[ 3  0  0 -3 -3]
A.echelon_form () 
        
[ 1  0  0 -1 -1]
[ 0  1 -2  0  0]
[ 0  0  0  0  0]
[ 0  0  0  0  0]
[ 1  0  0 -1 -1]
[ 0  1 -2  0  0]
[ 0  0  0  0  0]
[ 0  0  0  0  0]
#32 A= matrix([[1,1,2,8],[-1,-2,3,1],[3,-7,4,10]]) A 
        
[ 1  1  2  8]
[-1 -2  3  1]
[ 3 -7  4 10]
[ 1  1  2  8]
[-1 -2  3  1]
[ 3 -7  4 10]
A.echelon_form () 
        
[  1   0   7  17]
[  0   1  47  95]
[  0   0  52 104]
[  1   0   7  17]
[  0   1  47  95]
[  0   0  52 104]
#33 A= matrix([[2,2,2,0],[-2,5,2,0],[-7,7,1,0]]) A 
        
[ 2  2  2  0]
[-2  5  2  0]
[-7  7  1  0]
[ 2  2  2  0]
[-2  5  2  0]
[-7  7  1  0]
A.echelon_form () 
        
[1 1 1 0]
[0 7 4 0]
[0 0 0 0]
[1 1 1 0]
[0 7 4 0]
[0 0 0 0]
#34 A= matrix([[1,-1,2,-1,-1],[2,1,-2,-2,-2],[-1,2,-4,1,1],[3,0,0,-1,-3]]) A 
        
[ 1 -1  2 -1 -1]
[ 2  1 -2 -2 -2]
[-1  2 -4  1  1]
[ 3  0  0 -1 -3]
[ 1 -1  2 -1 -1]
[ 2  1 -2 -2 -2]
[-1  2 -4  1  1]
[ 3  0  0 -1 -3]
A.echelon_form () 
        
[ 1  0  0  1 -1]
[ 0  1 -2  0  0]
[ 0  0  0  2  0]
[ 0  0  0  0  0]
[ 1  0  0  1 -1]
[ 0  1 -2  0  0]
[ 0  0  0  2  0]
[ 0  0  0  0  0]
#35 A= matrix([[3,5,2],[4,2,3],[-1,2,4]]) A 
        
[ 3  5  2]
[ 4  2  3]
[-1  2  4]
[ 3  5  2]
[ 4  2  3]
[-1  2  4]
A.determinant () 
        
-69
-69
#36 A= matrix([[2,-3,-5],[1,0,4],[3,3,9]]) A 
        
[ 2 -3 -5]
[ 1  0  4]
[ 3  3  9]
[ 2 -3 -5]
[ 1  0  4]
[ 3  3  9]
A.determinant () 
        
-48
-48
#37 A= matrix([[1,2],[-1,3]]) A 
        
[ 1  2]
[-1  3]
[ 1  2]
[-1  3]
A.determinant () 
        
5
5
#38 A= matrix([[6,4],[3,2]]) A 
        
[6 4]
[3 2]
[6 4]
[3 2]
A.determinant () 
        
0
0
#39 A= matrix([[-1,7],[-8,-3]]) A 
        
[-1  7]
[-8 -3]
[-1  7]
[-8 -3]
A.determinant () 
        
59
59
#40 A= matrix([[1,-2,7],[3,5,1],[4,3,8]]) A 
        
[ 1 -2  7]
[ 3  5  1]
[ 4  3  8]
[ 1 -2  7]
[ 3  5  1]
[ 4  3  8]
A.determinant () 
        
0
0
#41 A= matrix([[8,2,-1],[-3,4,-6],[1,7,2]]) A 
        
[ 8  2 -1]
[-3  4 -6]
[ 1  7  2]
[ 8  2 -1]
[-3  4 -6]
[ 1  7  2]
A.determinant () 
        
425
425
#42 A= matrix([[1,0,3],[4,0,-1],[2,8,6]]) A 
        
[ 1  0  3]
[ 4  0 -1]
[ 2  8  6]
[ 1  0  3]
[ 4  0 -1]
[ 2  8  6]
A.determinant () 
        
104
104