CoCalc Shared FilesLab 3 / Lab3-turnin.sagewsOpen in CoCalc with one click!
Author: Jamie Lee
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# Lab 3:Linear Algebra # Name: Jamie Lee # 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 # use enough comments that you and the grader can understand your code.
# For lab 3, please do the linear algebra exercises 1-18 only
#1 vector([3, 10])
(3, 10)
#2 v=vector([-2, 7, 5])
type(v)
<type 'sage.modules.vector_integer_dense.Vector_integer_dense'>
#3 a=vector([4, 2]) b=vector([-1, 5])
#3.1 a+b
(3, 7)
#3.2 6*a
(24, 12)
#3.3 4*a+3*b
(13, 23)
#3.4 -b
(1, -5)
#3.5 -a+b
(-5, 3)
#3.6 3.14*a
(12.5600000000000, 6.28000000000000)
#4 v=vector([1, 2, 4]) plot(v) thickness=4
3D rendering not yet implemented
#5 #5.3.1 plot(a, color= "red")+plot(b, color= "blue")+plot(a+b, color= "purple")
#5.3.2 plot(a, color= "red")+plot(b, color= "blue")+plot(6*a, color= "purple")
#5.3.3 plot(a, color= "red")+plot(b, color= "blue")+plot(4*a+3*b, color= "purple")
#5.3.4 plot(a, color= "red")+plot(b, color= "blue")+plot(-b, color= "purple")
#5.3.5 plot(a, color= "red")+plot(b, color= "blue")+plot(-a+b, color= "purple")
#5.3.6 plot(a, color= "red")+plot(b, color= "blue")+plot(3.14*a, color= "purple")
#6 def lineartest(f): var("x, y, a") if f(a*x) == a*f(x) and f(x+y) == f(x)+f(y): return True else: return False
#7 f= 4*x print(lineartest(f))
True
f= 8+x print(lineartest(f))
False
f= x-10 print(lineartest(f))
False
#8 def f(v): l1= [4*v[0]+2*v[1], 3*v[0]-v[1]] v1= vector(l1) return(v1)
a= 1 b= 2 f ([1, 2]) f ([0, 0]) f ([2, 5])
(8, 1) (0, 0) (18, 1)
#9 def p(v): l2= [3*v[0]+5*v[1], 3*v[0]-2*v[1]] v2= vector(l2) return(v2) a1 = vector ([1,2]) a2 = vector ([0,3]) a3 = vector ([3,1]) b1 = p(a1) b2 = p(a2) b3 = p(a3) plot(b1, color = "red") + plot(b2, color = "green") + plot(b3, color = "blue") + plot(a1, color = "red", linestyle = "--") + plot(a2, color = "green", linestyle = "--") + plot(a3, color = "blue", linestyle = "--")
#10 def p(v): l1= [3*v[0]-8*v[1]-12*v[2], -3*v[0]+2*v[1]+5*v[2], 5*v[0]-6*v[1]+v[2]] v1= vector(l1) return(v1)
p(vector([1, 2, 3])) #test
(-49, 16, -4)
#11 def bears(p): pop = [0.57*p[0]+0.5025*p[1], 0.33*p[0]+0.917*p[1]] p1= vector(pop) return(p1)
bears(vector([1,1]))
(1.07250000000000, 1.24700000000000)
#12 bears(vector([13, 20]))
(17.4600000000000, 22.6300000000000)
#13 x1 = vector ([1,0]) x2 = vector ([0,1]) y1 = bears(x1) y2 = bears(x2) plot(x1, color = "red", aspect_ratio = 1) + plot(x2, color = "blue", aspect_ratio = 1) + plot(y1, color = "red", aspect_ratio = 1, linestyle = "--") + plot(y2, color = "blue", aspect_ratio = 1, linestyle = "--")
#The result shows the previous vectors increased by 13 and 20, respectively. #14 x1 = vector([1, 0]) x2 = vector([0, 1]) y1 = 13*bears(x1) y2 = 20*bears(x2) plot(x1, color = "red", aspect_ratio=1) + plot(x2, color = "blue", aspect_ratio = 1) + plot(y1, color = "red", aspect_ratio = 1, linestyle = "--") + plot(y2, color = "blue", aspect_ratio = 1, linestyle = "--")
#15 x1 = vector([1, 0]) x2 = vector([0, 1]) y1 = 1*bears(x1) y2 = 2*bears(x2) plot(x1, color = "red", aspect_ratio=1) + plot(x2, color = "blue", aspect_ratio = 1) + plot(y1, color = "red", aspect_ratio = 1, linestyle = "--") + plot(y2, color = "blue", aspect_ratio = 1, linestyle = "--")
x1 = vector([1, 0]) x2 = vector([0, 1]) y1 = 2*bears(x1) y2 = 1*bears(x2) plot(x1, color = "red", aspect_ratio=1) + plot(x2, color = "blue", aspect_ratio = 1) + plot(y1, color = "red", aspect_ratio = 1, linestyle = "--") + plot(y2, color = "blue", aspect_ratio = 1, linestyle = "--")
#16.a def ani(x): dog = [0.4*x[0]-3.43*x[1], 2*x[0]+4.3*x[1]] cat = vector(dog) return cat
x1 = vector([1, 0]) x2 = vector([0, 1]) y1 = ani(x1) y2 = ani(x2) plot(x1, color = "red", aspect_ratio=1) + plot(x2, color = "blue", aspect_ratio = 1) + plot(y1, color = "red", aspect_ratio = 1, linestyle = "--") + plot(y2, color = "blue", aspect_ratio = 1, linestyle = "--")
x1 = vector([1, 0]) x2 = vector([0, 1]) y1 = 5*ani(x1) y2 = 10*ani(x2) plot(x1, color = "red", aspect_ratio=1) + plot(x2, color = "blue", aspect_ratio = 1) + plot(y1, color = "red", aspect_ratio = 1, linestyle = "--") + plot(y2, color = "blue", aspect_ratio = 1, linestyle = "--")
#16.b def sea(x): fish = [-0.4*x[0]+3.43*x[1], -2*x[0]-4.3*x[1]] shark = vector(fish) return shark
x1 = vector([1, 0]) x2 = vector([0, 1]) y1 = sea(x1) y2 = sea(x2) plot(x1, color = "red", aspect_ratio=1) + plot(x2, color = "blue", aspect_ratio = 1) + plot(y1, color = "red", aspect_ratio = 1, linestyle = "--") + plot(y2, color = "blue", aspect_ratio = 1, linestyle = "--")
x1 = vector([1, 0]) x2 = vector([0, 1]) y1 = 5*sea(x1) y2 = 10*sea(x2) plot(x1, color = "red", aspect_ratio=1) + plot(x2, color = "blue", aspect_ratio = 1) + plot(y1, color = "red", aspect_ratio = 1, linestyle = "--") + plot(y2, color = "blue", aspect_ratio = 1, linestyle = "--")
#17 def bears(p): pop = [0.57*p[0]+0.5025*p[1], 0.33*p[0]+0.917*p[1]] p1= vector(pop) return(p1)
xb = bears(vector([1, 0])) yb = bears(vector([0, 1]))
#18 m = column_matrix([xb, yb]) m
[0.570000000000000 0.502500000000000] [0.330000000000000 0.917000000000000]