<jupyter_start><jupyter_text>Final Exam Problem 1<jupyter_code>import numpy as np
A = np.array([[1,1,1],[1,0,4],[0,0,5]])
B = np.array([[89],[89],[95]])
C = np.linalg.inv(A).dot(B)
print(C)<jupyter_output>[[13.]
 [57.]
 [19.]]<jupyter_text>Problem 2<jupyter_code>A = np.array([[3,-1,1],[9,-3,3],[-12,4,-4]])
B = np.array([[5],[15],[-20]])
print(A)
print (B)
Ainv = np.linalg.pinv(A)
X = Ainv.dot(B)
print(X)<jupyter_output>[[  3  -1   1]
 [  9  -3   3]
 [-12   4  -4]]
[[  5]
 [ 15]
 [-20]]
[[ 1.36363636]
 [-0.45454545]
 [ 0.45454545]]<jupyter_text>Problem 3<jupyter_code>from numpy.linalg import eig
A = np.array([[8,5,-6],[-12,-9,12],[-3,-3,5]])
print(A)
w,v = np.linalg.eig(A) 
print("The eigenvalue/s are:",w.round())
print("The eigenvector/s are:\n",v.round())<jupyter_output>[[  8   5  -6]
 [-12  -9  12]
 [ -3  -3   5]]
The eigenvalue/s are: [-1.  3.  2.]
The eigenvector/s are:
 [[ 0. -1.  1.]
 [-1.  1.  0.]
 [-0. -0.  1.]]
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