<jupyter_start><jupyter_text>Question 1<jupyter_code>import numpy as np
#made a square matrix with the lenght of 5
A=np.array([[1,2,3,4,5],[6,7,8,9,10],[10,9,8,7,6],[5,4,3,2,1],[1,3,5,7,9]])
#prints the 5 lenght matrix
print(A)<jupyter_output>[[ 1  2  3  4  5]
 [ 6  7  8  9 10]
 [10  9  8  7  6]
 [ 5  4  3  2  1]
 [ 1  3  5  7  9]]<jupyter_text>Question 2<jupyter_code>#made a square matrix which the elements below the principal diagonal are zero
A = np.array([[1,1,1,1],[0,1,1,1],[0,0,1,1],[0,0,0,1]])
#prints the matrix
print(A)<jupyter_output>[[1 1 1 1]
 [0 1 1 1]
 [0 0 1 1]
 [0 0 0 1]]<jupyter_text>Question 3<jupyter_code>#made a symmetrical matrix
A=np.array([[2,4,6],[4,8,10],[6,10,2]])
#prints the symmetrical matrix
print(A)<jupyter_output>[[ 2  4  6]
 [ 4  8 10]
 [ 6 10  2]]<jupyter_text>Question 4<jupyter_code>#inputted the given matrix
A=np.array([[1,2,3],[2,3,3],[3,4,-2]])
#Gets the inverse of the given Matrix which is declared as A
B=(np.linalg.inv(A))
#prints the inverse of the matrix
print(B)<jupyter_output>[[-3.6  3.2 -0.6]
 [ 2.6 -2.2  0.6]
 [-0.2  0.4 -0.2]]<jupyter_text>Question 5<jupyter_code>#inputs the given matrix
A=np.array([[1,2,3],[2,3,3],[3,4,-2]])
#prints the given matrix
print(A)
#gets the determinant of the given matrix
print(np.linalg.det(A))
#gets the round off of it
print(round(np.linalg.det(A)))<jupyter_output>[[ 1  2  3]
 [ 2  3  3]
 [ 3  4 -2]]
5.000000000000001
5<jupyter_text>Question 6<jupyter_code>#inputs the given
A = np.array([[5,4,1],[10,9,4],[10,13,15]])
B = np.array( [[3.4],[8.8],[19.2]])
#gets the root of given
C = np.linalg.inv(A) @ B
#prints the root
print(C)<jupyter_output>[[0.2]
 [0.4]
 [0.8]]
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