SharedMath_240 / Section1.6_Max.sagewsOpen in CoCalc
Section 1.6 Homework
### Question 5

q = matrix([[2,0,-1,0,0],[3,0,0,-1,0],[0,2,-3,-2,0],[0,1,-3,0,0]])
q.rref()

[ 1 0 0 -1/3 0] [ 0 1 0 -2 0] [ 0 0 1 -2/3 0] [ 0 0 0 0 0]

###  Question 6

r = matrix([[3,0,0,-1,0],[1,0,-2,0,0],[4,6,-8,-3,0],[0,1,-3,0,0],[0,2,0,-1,0]])
r.rref()

[ 1 0 0 -1/3 0] [ 0 1 0 -1/2 0] [ 0 0 1 -1/6 0] [ 0 0 0 0 0] [ 0 0 0 0 0]

###   Question 7

s = matrix([[1,0,-3,0,0,0],[1,8,-5,-2,0,0],[1,6,-6,0,-1,0],[3,7,-7,-1,-2,0]])
s.rref()

[ 1 0 0 0 -1 0] [ 0 1 0 0 -1/3 0] [ 0 0 1 0 -1/3 0] [ 0 0 0 1 -1 0]

###   Question 8

t = matrix([[1,0,0,0,-2,0,0],[1,1,0,-1,0,0,0],[4,4,1,-2,-4,-4,0],[0,1,0,0,-1,-1,0],[0,0,2,0,0,-2,0]])
t.rref()

[ 1 0 0 0 0 -1 0] [ 0 1 0 0 0 -3/2 0] [ 0 0 1 0 0 -1 0] [ 0 0 0 1 0 -5/2 0] [ 0 0 0 0 1 -1/2 0]

###   Question 9

u = matrix([[1,0,-3,0,0,0,0],[6,0,0,0,0,-1,0],[0,1,0,-2,0,0,0],[0,2,0,0,-1,0,0],[0,8,-4,-3,-2,-1,0]])
u.rref()

[ 1 0 0 0 0 -1/6 0] [ 0 1 0 0 0 -22/45 0] [ 0 0 1 0 0 -1/18 0] [ 0 0 0 1 0 -11/45 0] [ 0 0 0 0 1 -44/45 0]

###   Question 10

v = matrix([[1,0,0,-1,0,0,0,0],[1,0,1,0,0,-3,0,0],[0,2,0,0,-1,0,0,0],[0,10,0,0,0,-1,0,0],[0,35,4,-4,0,-12,-1,0],[0,0,2,-1,-3,0,-2,0]])
v.rref()

[ 1 0 0 0 0 0 -16/327 0] [ 0 1 0 0 0 0 -13/327 0] [ 0 0 1 0 0 0 -374/327 0] [ 0 0 0 1 0 0 -16/327 0] [ 0 0 0 0 1 0 -26/327 0] [ 0 0 0 0 0 1 -130/327 0]

###   Question 11 done on paper
z = matrix([[1,0,1,0,20],[0,1,-1,-1,0],[-1,-1,0,0,80]])
z.rref()

###   Question 12

w = matrix([[1,0,-1,-1,0,40],[-1,-1,0,0,0,-200],[0,1,1,0,-1,100],[0,0,0,1,1,60]])
w.rref()

[ 1 0 1 0 20] [ 0 1 -1 0 -100] [ 0 0 0 1 -100] [ 1 0 -1 0 1 100] [ 0 1 1 0 -1 100] [ 0 0 0 1 1 60] [ 0 0 0 0 0 0]

###   Question 13

x = matrix([[-1,1,0,0,0,0,50],[0,-1,1,-1,1,0,0],[0,0,0,0,-1,1,-60],[0,0,0,1,0,-1,50],[1,0,-1,0,0,0,-40]])
x.rref()

[ 1 0 -1 0 0 0 -40] [ 0 1 -1 0 0 0 10] [ 0 0 0 1 0 -1 50] [ 0 0 0 0 1 -1 60] [ 0 0 0 0 0 0 0]

###   Question 14

y = matrix([[1,-1,0,0,0,0,100],[0,1,-1,0,0,0,-50],[0,0,1,-1,0,0,120],[0,0,0,1,-1,0,-150],[0,0,0,0,1,-1,80],[-1,0,0,0,0,1,-100]])
y.rref()

[ 1 0 0 0 0 -1 100] [ 0 1 0 0 0 -1 0] [ 0 0 1 0 0 -1 50] [ 0 0 0 1 0 -1 -70] [ 0 0 0 0 1 -1 80] [ 0 0 0 0 0 0 0]