How to get a matrix with 10 rows if the input matrix has 784 rows?

Question

Neural networks

In the digit recognition example, a 784x1 matrix is ​​input to the network, and a 10x1 matrix is
​​output. How do they achieve this? Only one thought comes to me that I need to transpose the matrix.
For example.
The network consists of three layers.
Input matrix = 784x1
First layer = 1x100 matrix
Hidden layer = 100x10 matrix
Output layer = 10x1 matrix
The result of multiplying the input matrix by the layer: 784x1 * 1x100 = 784x10
The result of multiplying the first layer by the hidden: 784x10 * 100x10 = 784x10, transpose and get \u003d 10x784
The result of multiplying the hidden layer by the output: 10x784 * 10x1 \u003d 10x1
However, it feels like this is not the way of the Jedi and there is a better way.
The best way is to just transpose the input matrix ?

Answer 1

Haven't you seen perceptron pictures similar to this one:
From each of 784 to each of 10 there is a connection with its own weight. This is one layer. There are more layers in a real network.