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ubuntu2004
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Kernel: SageMath 9.7
100/(vec_length((0,0.9,0)) * sqrt(1 - dot_product((0,0.9,0), (0,-5,3))/(vec_length((0,0.9,0)) * vec_length((0,-5,3)))*dot_product((0,0.9,0), (0,-5,3))/(vec_length((0,0.9,0)) * vec_length((0,-5,3)))));
--------------------------------------------------------------------------- NameError Traceback (most recent call last) Input In [1], in <cell line: 1>() ----> 1 Integer(100)/(vec_length((Integer(0),RealNumber('0.9'),Integer(0))) * sqrt(Integer(1) - dot_product((Integer(0),RealNumber('0.9'),Integer(0)), (Integer(0),-Integer(5),Integer(3)))/(vec_length((Integer(0),RealNumber('0.9'),Integer(0))) * vec_length((Integer(0),-Integer(5),Integer(3))))*dot_product((Integer(0),RealNumber('0.9'),Integer(0)), (Integer(0),-Integer(5),Integer(3)))/(vec_length((Integer(0),RealNumber('0.9'),Integer(0))) * vec_length((Integer(0),-Integer(5),Integer(3)))))) NameError: name 'vec_length' is not defined 


#question 8
a1 = vector([2, 1, 1])
a2 = vector([0, 1, -1])
b = vector([3, 3, 3])
yhat = a1*((a1*b)/(a1*a1))+a2*((a2*b)/(a2*a2))
yhat
(4, 2, 2)

question 9

a1 = vector([2, -1, 0]) a2 = vector([2, 4, -5]) y = vector([5, 5, -3]) yhat = a1*((ya1)/(a1a1))+a2*((ya2)/(a2a2)) (y-yhat).norm()



#question 10
v1 = vector([1, 2, 1])
v2 = vector([5, 0, 1])
v2 - v1*((v2*v1)/(v1*v1))
(4, -2, 0)


#question 11
R = Matrix([[1, 1], [0, 4]])
qtb = vector([17, 18])
R.inverse()*qtb
(25/2, 9/2)


#question 18
y = vector([3, 10])
v = vector([1, 0])
yhat = v*((y*v)/(v*v))
(y-yhat).norm()
10
#question 3
v = 2 * vector([3, 6, 2])
v.norm()
14


#quesiton 20
u = 6
v = 8
sqrt(u^2 + v^2)
10


#question 16
x = Matrix([[1, 2, 3, 4], [1, 1, 1, 1]])
y = vector([7, -2, 1, 4])
x*y
(22, 10)
#question 13
A = Matrix([[0, 4], [4, 0], [0, 1]])
b = vector([2, 4, 16])
((A.transpose()*A)).solve_right((A.transpose()*b))
(1, 24/17)