Hands-On Mathematics for Deep Learning

Solving linear equations in n-dimensions

Now that we've dealt with linear equations in 2-dimensions and have developed an understanding of them, let's go a step further and look at equations in 3-dimensions.

Earlier, our equations produced curves in the 2-dimensional space (xy-plane). Now, the equations we will be dealing with will produce planes in 3-dimensional space (xyz-plane).

Let's take an arbitrary 3x3 matrix, as follows:

We know from earlier in having dealt with linear equations in two dimensions that our solution b, as before, is a linear combination of the three column vectors, so that .

The equation (equation 1) produces a plane, ...