Скачать или смотреть Simultaneous linear equations and their possible solutions | Matrices | Guide to Engineering Maths

In this video I discuss the possible solutions to two simultaneous equations. It is important to keep these in mind when understanding and describing simultaneous equations using matrix algebra. Although in this video I keep things simple by only talking about two equations, a system of linear equations can have as many equations and variables in it as you like. We will be dealing with systems of 3 and more linear equations later on in the Guide to Engineering Maths.

A few definitions/descriptive words that I've found helpful to understand:

Linear:
Think straight lines. Simply put, it means whatever it is (usually an equation, function or transformation) doesn't create curves or irregular spaces. So f(x) = x^2 is not a linear function neither is y^2 + sin(x) = 5, but x + 3y - 2z = 9 is.
In essence an equation is linear if it's variables are only multiplied by constants (commonly real numbers), and each variable is to the power of 1. In conversation, if I were to say that, "the amount of torque about a point is 'linearly' proportional to the force applied", I would be saying the Torque = (Some constant) x the force applied.

Linear dependence/independence:
Well this can be deciphered from knowing what linear means... If two things are 'linearly' independent then they cannot be described as a scalar multiple of each other. They are 'independent' of each other 'linearly'.
And so if they are linearly dependent then they can be described as a scalar multiple of each other.

Intro music by an amazing band called Wordy, check them out here:
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