<jupyter_start><jupyter_text>**<NAME>** 201914430<jupyter_code>#Problem #1
#-x+z=6
#-y+3z=0
#x+y+z=89

import numpy as np
A=np.array([[-1,0,1],[0,-1,3],[1,1,1]]) #matrix A
print(A)
A_inv=np.linalg.inv(A) #inverse of matrix A
print(A_inv)
B=np.array([[6],[0],[89]])#Constants
print(B)
X=np.dot(A_inv,B) #dot product of inversed matrix A and constants to get the missing variables x,y,z
print(X)<jupyter_output>[[13.]
 [57.]
 [19.]]<jupyter_text>Final Answer: Student A has 13 cash, Student B has 57 cash, and Student C has 19 cash for a total of 89 cash.<jupyter_code>#Problem #2

import numpy as np
from scipy.linalg import solve
A = np.array([[3,-1,1],[9,-3,3],[-12,4,-4]])
B = np.array([[5],[15],[-20]])
print(A)
print(B)
X=np.linalg.solve(A,B)
print(X)<jupyter_output>[[  3  -1   1]
 [  9  -3   3]
 [-12   4  -4]]
[[  5]
 [ 15]
 [-20]]<jupyter_text>Explanantion: The error occured because the determinant of the matrix A is equal to zero, which made the matrix A a singular matrix, meaning it has no inverse such that it has no multiplicative inverse.<jupyter_code>#Problem 3
A=np.array([[8,5,-6],[-12,-9,12],[-3,-3,5]])
print(A)
s,t=np.linalg.eig(A)
print("Eigenvalues:",s.round())
print("Eigenvectors: ",t.round())<jupyter_output>[[  8   5  -6]
 [-12  -9  12]
 [ -3  -3   5]]
Eigenvalues: [-1.  3.  2.]
Eigenvectors:  [[ 0. -1.  1.]
 [-1.  1.  0.]
 [-0. -0.  1.]]
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