quiz5.ipynb

Kernel: SageMath 7.4

C=matrix (QQ,4,[-2,-5,-10,3,10,1,3,6,-2,-7,1,2,4,0,0,0,1,2,-3,10])
print"a"
print C

a
[ -2  -5 -10   3  10]
[  1   3   6  -2  -7]
[  1   2   4   0   0]
[  0   1   2  -3  10]

print"b"
C.swap_rows(0,1)
C.add_multiple_of_row(1,0,2)
C.add_multiple_of_row(2,0,-1)
print C

b
[  0   1   2  -1  -4]
[  1   5  10  -4 -15]
[  0  -2  -4   3  11]
[  0   1   2  -3  10]

print"c"
print C.rref()
print "x1= 2"
print "x2 = -1 - 2x3"
print "x3 = x3"
print "x4 = 3"

c
[1 0 0 0 0]
[0 1 2 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
x1= 2
x2 = -1 - 2x3
x3 = x3
x4 = 3

print "d"
C=matrix (QQ,4,[-2,-5,-10,3,10,1,3,6,-2,-7,1,2,4,0,0,0,1,2,-3,10])
A=C.submatrix(0,0,4,4)
print A

d
[ -2  -5 -10   3]
[  1   3   6  -2]
[  1   2   4   0]
[  0   1   2  -3]

print "e"
print 3*A*A.transpose()

e
[ 414 -249 -156 -102]
[-249  150   93   63]
[-156   93   63   30]
[-102   63   30   42]

print "f"
print 1/2*(A-A.transpose())+1/2*(A+A.transpose())

f
[ -2  -5 -10   3]
[  1   3   6  -2]
[  1   2   4   0]
[  0   1   2  -3]

print "problem 2a"
P = polygon([(0,0),(0,1),(1,1),(1,0)])
plot(P)