213 - A10 - Basis

184 days ago by Professor213

var('k') a = vector([7,-5,0]) b = vector([-7,1,-7]) c = vector([-7,-11,k]) d = vector([0,0,1]) 
       
       
(0, 0, 1)
(0, 0, 1)
mat = matrix([a,b,c,d]).transpose() mat 
       
[  7  -7  -7   0]
[ -5   1 -11   0]
[  0  -7   k   1]
[  7  -7  -7   0]
[ -5   1 -11   0]
[  0  -7   k   1]
mat.echelon_form() 
       
[          1           0           0 -3/(k + 28)]
[          0           1           0 -4/(k + 28)]
[          0           0           1  1/(k + 28)]
[          1           0           0 -3/(k + 28)]
[          0           1           0 -4/(k + 28)]
[          0           0           1  1/(k + 28)]
# column space A = matrix([[4,-3,-10,-7,10],[1,0,-1,-1,1],[-1,0,1,1,-1],[10,-6,-21,-16,22],[20,-12,-42,-32,44]]).transpose() A 
       
[  4   1  -1  10  20]
[ -3   0   0  -6 -12]
[-10  -1   1 -21 -42]
[ -7  -1   1 -16 -32]
[ 10   1  -1  22  44]
[  4   1  -1  10  20]
[ -3   0   0  -6 -12]
[-10  -1   1 -21 -42]
[ -7  -1   1 -16 -32]
[ 10   1  -1  22  44]
A.echelon_form() 
       
[ 1  1 -1  0  0]
[ 0  3 -3  0  0]
[ 0  0  0  1  2]
[ 0  0  0  0  0]
[ 0  0  0  0  0]
[ 1  1 -1  0  0]
[ 0  3 -3  0  0]
[ 0  0  0  1  2]
[ 0  0  0  0  0]
[ 0  0  0  0  0]