Please, could you do on paper, what this training example should look like? For both separately, PCA and LDA.

You can use arbitrary data from such a problem and show it in 1D or 2D.

When considering algorithms such as PCA, LDA, and Regression ("Linear curve fitting"): 1. Draw the data from such a problem setting in 1d or 2d (see for example what it looked like in the exercises). 2. Figure out what you are even trying to do with that data (what's the w supposed to do?). 3. Write down i) the objective we want to minimize to obtain the optimal w and ii) how we use w to solve our task from 2 .) 4. Think about what an optimal w should look like for your drawn example, and add it to your sketch. Finally, go over how we actually estimate w from the data (i.e. w^= formula )