What does a neuron compute?

A neuron computes a function g that scales the input x linearly (Wx + b)

A neuron computes a linear function (z = Wx + b) followed by an activation function

A neuron computes the mean of all features before applying the output to an activation function

Explanation :

Correct, we generally say that the output of a neuron is a = g(Wx + b) where g is the activation function (sigmoid, tanh, ReLU, ...).

Recall that "np.dot(a,b)" performs a matrix multiplication on a and b, whereas "a*b" performs an element-wise multiplication. Consider the two following random arrays "a" and "b": a = np.random.randn(12288, 150) # a.shape = (12288, 150)
b = np.random.randn(150, 45) # b.shape = (150, 45)
c = np.dot(a,b)

Explanation :

Correct, remember that a np.dot(a, b) has shape (number of rows of a, number of columns of b). The sizes match because :

"number of columns of a = 150 = number of rows of b"

Consider the following code:What will be c? (If you’re not sure, feel free to run this in python to find out). a = np.random.randn(3, 3)
b = np.random.randn(3, 1)
c = a*b

This will invoke broadcasting, so b is copied three times to become (3,3), and *∗ is an element-wise product so c.shape will be (3, 3)

This will invoke broadcasting, so b is copied three times to become (3, 3), and *∗ invokes a matrix multiplication operation of two 3x3 matrices so c.shape will be (3, 3)

Explanation :
```
A is correct
```

Suppose you have n_x input features per example. Recall that \( X = [x^{(1)} x^{(2)} ... x^{(m)}] \). What is the dimension of X?

Explanation :

Consider the two following random arrays "a" and "b": What will be the shape of "c"?
a = np.random.randn(4, 3) # a.shape = (4, 3)
b = np.random.randn(3, 2) # b.shape = (3, 2)
c = a*b

The computation cannot happen because the sizes don't match. It's going to be "Error"!

Explanation :

Indeed! In numpy the "*" operator indicates element-wise multiplication. It is different from "np.dot()". If you would try "c = np.dot(a,b)" you would get c.shape = (4, 2).

Consider the two following random arrays "a" and "b": What will be the shape of "c"?
a = np.random.randn(2, 3) # a.shape = (2, 3)
b = np.random.randn(2, 1) # b.shape = (2, 1)
c = a + b

Explanation :

Yes! This is broadcasting. b (column vector) is copied 3 times so that it can be summed to each column of a.

Suppose img is a (32,32,3) array, representing a 32x32 image with 3 color channels red, green and blue. How do you reshape this into a column vector?

Explanation :
```
x = img.reshape((32*32*3,1))
```

Which of these is the "Logistic Loss"?

L⁽ⁱ⁾(yhat⁽ⁱ⁾, y⁽ⁱ⁾) = |y⁽ⁱ⁾) - yhat⁽ⁱ⁾)|²

L⁽ⁱ⁾(yhat⁽ⁱ⁾, y⁽ⁱ⁾) = -(y⁽ⁱ⁾log(yhat⁽ⁱ⁾)) + (1 - y⁽ⁱ⁾)log(1-yhat⁽ⁱ⁾)

Explanation :

 this is the logistic loss or cross entropy loss

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