 SharedLab 06 / Lab6-turnin.sagewsOpen in CoCalc
Author: Janeane Kim
# Lab 6

# Name: Janeane M. Kim
# I worked on this code with:

# Please do all of your work for this week's lab in this worksheet. If
# you wish to create other worksheets for scratch work, you can, but
# this is the one that will be graded. You do not need to do anything
# to turn in your lab. It will be collected by your TA at the beginning
# of (or right before) next week’s lab.

# Be sure to clearly label which question you are answering as you go and to

# 43
@interact
def interact1(R=(-10,10), S=(-10,10),target=vector([1,1])):
# defines a function with the changing variables
u=R*(vector([1,2]))
# gives u the multipled variable
v=S*(vector([1,1/2]))
p=plot(u+v, color="red")+plot(u)+plot(v)
# plots the sum of all the variables
f=text(str(((u+v), (u+v))), u+v, fontsize=15, color="red")
show(p+f)

# (R,S) is around (1.28,0.8) when the sum vector is (2,3)

# PLEASE restart and replay the code if an error message occurs! Thank you
# turns out there's something wrong(?)
# cannot process interacts with more than one variable without restarting the wksht immediately before

# 44
@interact
def interact(R=(-10,10), S=(-10,10),target=vector([1,1])):
# defines a function with the changing variables
u=R*(vector([2,5]))
# gives u the multipled variable
v=S*(vector([0.6,9]))
p=plot(u+v, color="red")+plot(u)+plot(v)
# plots the sum of all the variables
f=text(str(((u+v), (u+v))), u+v, fontsize=15, color="red")
show(f+p)

# 45
@interact
def interact(R=(-10,10), S=(-10,10),target=vector([1,1])):
# defines a function with the changing variables
u=R*(vector([1,0]))
# gives u the multipled variable
v=S*(vector([0,1]))
p=plot(u+v, color="red")+plot(u)+plot(v)
# plots the sum of all the variables
f=text(str(((u+v), (u+v))), u+v, fontsize=15, color="red")
show(f+p)

# making u and v scalar multiples of themselves lead to u and v missing parts of the vector

# 46
trix=matrix([[1,1],[2,1/2]])
trix

[ 1 1] [ 2 1/2]
# 47
sample=vector([1.28,0.8])
trix*sample

(2.08000000000000, 2.96000000000000)
# when multiplied by the given matrix, the derived R,S coordinates become close to the original X,Y point (2,3)

# 48
# original XY point:(4.5,7)
areforkids=vector([3.12,1.4])
trix*areforkids

(4.52000000000000, 6.94000000000000)
# original XY point (-3,5)
yogurt=vector([-2.28, -0.64])
trix*yogurt

(-2.92000000000000, -4.88000000000000)
# 49
W=matrix([[-1/3,2/3],[4/3,-2/3]])
W

[-1/3 2/3] [ 4/3 -2/3]
# 50
(vector([-3,5]))*W

(23/3, -16/3)
# 51
# original XY point (-5,-9)
yogurt=vector([-4.38, -0.64])
trix*yogurt

(-5.02000000000000, -9.08000000000000)
# 52
trix.inverse()

(-3.02000000000000, -5.08000000000000) [-1/3 2/3] [ 4/3 -2/3]
# 53
# the T inverse is the same as the manually derived W
# 54
M=matrix([[7,-4],[4,-3]])
M.eigenvectors_right()

[(5, [ (1, 1/2) ], 1), (-1, [ (1, 2) ], 1)]
# the corresponding eigenvalues of this matrix are 5, 1, and -1
︠a7f91e7e-c1f4-4859-8cc0-5664e1c48847︠
# 55