Corrections for M4ML C1 W2 UGL solving linear systems in 3 variables

Just a few suggestions/corrections for the Ungraded Lab about solving linear equations.

Introduction

* Use `NumPy` linear algebra package to find the solutions to the system of linear equations
* Perform row reduction to bring matrix into row echelon form
* Find the solution for the system of linear equations using row reduced matrix
* Evaluate the determinant of the matrix to see again the connection between matrix singularity and the number of solutions of the linear system

I think the following sounds more like natural English (just a few minor wording tweaks):

* Use the `NumPy` linear algebra package to find the solutions to a system of linear equations
* Perform row reduction to bring a matrix into row echelon form
* Find the solution for a system of linear equations by using a row reduced matrix
* Evaluate the determinant of a matrix to see the connection between matrix singularity and the number of solutions of the linear system

Section 1.2

each column will correspond to the variable π‘₯1, π‘₯2, π‘₯3.

I think it sounds better to say:

each column will correspond to the variables π‘₯1, π‘₯2, π‘₯3.

Section 1.3

Let's calculate the determinant using np.linalg.det(A) function:

This construct appears in a number of places and I don’t have the energy to document all of them, but the more natural way to write that would be:

Let's calculate the determinant using the np.linalg.det(A) function:

But I guess maybe since the audience includes a lot of students who are not native English speakers, maybe it makes them feel more comfortable when they see the signs that the author is also not a native English speaker. :grinning: So I submit all this for your judgement: do what feels right to you and feel free to ignore my nit-picking.

Please, note that its value is non-zero, as expected.

I think it would look more normal to omit the first comma there:

Please note that its value is non-zero, as expected.

Section 2.3

the arithmetics of operations is easier then

I think the following would sound better:

the arithmetic of the operations is easier then

Or maybe even:

the arithmetic of the operations will be easier then

(Pro-forma anti-nanny reply.)