# Matrix Multiplication Question

In the matrix multiplication example where Andrew is showing multiplying Atranspose [200 17] by a 3x2 matrix W, the output is a 1 by 3 matrix which then has the sigmoid function applied to give [1 0 1]. My question is, what does that mean practically? I thought the point was to come to the a conclusion of 1 or 0, not a 1 by 3 matrix?

I’m assuming it needs to go into the 2nd layer to output a scalar but I don’t see how that’s done in the course thus far. Thanks in advance.

If there are three units in the hidden layer, you’re going to get three outputs.

Note that technically they are floating point values between 0 and 1 - not just 0 or 1.

The hidden layer outputs are combined in the output layer.

Thanks TMosh. Does that output of [1 0 1] go into the final/purple layer then to give a scalar? I’m assuming this example does not end at [1 0 1] is what I’m getting at.

Layer 1 output is a 1x3 matrix of float values between 0 and 1 each, which are “predictions” from each neuron on layer 1. Those floats are then fed to level 2 to produce the final prediction, which is a single float value between 0 to 1, that can be converted to boolean true or false or just fixed point 1 and 0 values using some threshold.

Yes.

Imagine each neuron as a judge and the layers as a jury of members. Each time they are given a question or a situation, they give a response. Imagine the juries sitting in their benches and their reply is the value they present - the value presenting is the matrix based on their position.

In response to how the matrix data goes from one layer to the other and if they flow, when the verdict is given from a set of juries (neurons) - they can be passed to a court of higher importance (maybe the High Court). Now the verdict can be from a single court or from multiple courts. Thus the resultant matrix to the output layer can be a scalar matrix or a vector matrix having both rows and columns.

Beautifully said thank you.

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