<jupyter_start><jupyter_text>**Problem 1** a. WY<jupyter_code>import numpy as np
np.dot(W,Y)<jupyter_output><empty_output><jupyter_text>b. Z+Z<jupyter_code>Z = np.array([[0,1],[2,3]])
Z = np.array([[0,1],[2,3]])
print(Z+Z)<jupyter_output>[[0 2]
 [4 6]]<jupyter_text>c. 3X<jupyter_code>X = np.array([[3,2,1],[-1,2,3],[2,-1,1]])
print(3*X)<jupyter_output>[[ 9  6  3]
 [-3  6  9]
 [ 6 -3  3]]<jupyter_text>**Problem 2** a. The product (YW)² is not defined<jupyter_code>YW = np.dot(Y,W)
print(np.square(YW))
#The statement is False since the following equation is defined.<jupyter_output>[[25 49]
 [16 16]]<jupyter_text>b. WY – X =<jupyter_code>A = np.dot(W,Y)
X = np.array([[3,2,1],[-1,2,3],[2,-1,1]])
print(A-X)
#As a result, the statement is True.<jupyter_output>[[-2  3 -7]
 [ 3  4 -7]
 [ 1  6  1]]<jupyter_text>c. YW – Z² =<jupyter_code>YW = np.dot(Y,W)
print(YW- np.square(Z))
#As a result, the statement is False.<jupyter_output>[[ 5 -8]
 [ 0 -5]]
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