(a) Verify that c1=[0,0,3], c2=[0,3,0], c3=[3,0,0] are linearly independent vectors.
(a) Verify that c1=[0,0,3], c2=[0,3,0], c3=[3,0,0] are linearly independent vectors.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Pyhton Help）Linear Independence
![(a) Verify that c1= [0,0,3], c2= [0,3,0], c3=[3,0,0] are linearly independent vectors.
Note: An explanation (~100 words) should be enough.
(b) Recall the definition of orthonormal vectors. Show that the following set forms an orthonormal vectors coding a new function in
Python which returns whether a given set is orthonormal or not.
5
6
1
1
##defining the required packages and the vectors to be checked.
2
import numpy as np
3 from numpy import linalg
4 ##defining the above vectors.
5
A = np.array((1/np.sqrt(2), 0,1/np.sqrt(2)))
6
B = np.array((0,1,0))
7
C = np.array((-1/np.sqrt(2),0,1/np.sqrt(2)))
√2
1#The function takes in 3 input 3D vectors and computes whether they are orthonormal or not.
2 #The function will output 1 if its orthonormal, and 0 if not.
3 def orthonormal_vectors (a,b,c):
##write your code
SHOSE
4 F ##HINT: sometimes, python can overcalculate the results for real numbers like square roots etc. it is fine to
use np.isclose() function
here
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa98117fc-4537-4efb-9016-9993926a8208%2F0187a9cb-0c0c-48a3-ab09-f42eeb355d04%2Fv7zvtyb_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Verify that c1= [0,0,3], c2= [0,3,0], c3=[3,0,0] are linearly independent vectors.
Note: An explanation (~100 words) should be enough.
(b) Recall the definition of orthonormal vectors. Show that the following set forms an orthonormal vectors coding a new function in
Python which returns whether a given set is orthonormal or not.
5
6
1
1
##defining the required packages and the vectors to be checked.
2
import numpy as np
3 from numpy import linalg
4 ##defining the above vectors.
5
A = np.array((1/np.sqrt(2), 0,1/np.sqrt(2)))
6
B = np.array((0,1,0))
7
C = np.array((-1/np.sqrt(2),0,1/np.sqrt(2)))
√2
1#The function takes in 3 input 3D vectors and computes whether they are orthonormal or not.
2 #The function will output 1 if its orthonormal, and 0 if not.
3 def orthonormal_vectors (a,b,c):
##write your code
SHOSE
4 F ##HINT: sometimes, python can overcalculate the results for real numbers like square roots etc. it is fine to
use np.isclose() function
here
=
Transcribed Image Text:In -
1 ##defining the required packages and the vectors to be checked.
2
import numpy as np.
from numpy import linalg
In
In
3
4
5
6
7
##defining the above vectors.
A = np.array((1/np.sqrt(2),0,1/np. sqrt(2)))
B = np.array((0,1,0))
C = np.array((-1/np.sqrt(2), 0,1/np.sqrt(2)))
5
6
7
1#The function takes in 3 input 3D vectors and computes whether they are orthonormal or not.
2
#The function will output 1 if its orthonormal, and 0 if not.
3 def orthonormal_vectors (a,b,c):
48 ##HINT: sometimes, python can overcalculate the results for real numbers like square roots etc. it is fine to
use np.isclose() function
8 A
5
6
70
8
9
##write your code ...... here
#return whether they form an orthonormal vectors or not (the output variable has to return 0 or 1 based on the
conditions) (fill in the value or variable in ... to return the value)
return
1# Do not change code below - Just run this cell after running the cell above.
2 #on successful implementation it must output 'Success'
3 try:
4
if orthonormal_vectors (A, B, C) == 1:
print('Success')
else:
print('Failure')
06 A 3 A 19 16
except:
print('Incomplete implementation')
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