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Solving systems of equations with matrices Video transcript Voiceover: I have a system of 2 equations with 2 unknowns here. We've seen how to solve this, and there's multiple writing a matrix in latex we've used, substitution, elimination, and we could do that right over here.

In fact, you could just add the two.

The left sides of the equations and the right sides of the equations, the s's would cancel out. Actually, let's just do it to show how that's relatively straightforward, for at least this example right over here.

You add the left-hand sides. You're left with negative t. Negative t is equal to 7 plus negative 6 is equal to 1, or you get the t is equal to negative 1. If t is equal to negative 1, this top equation, you could use either one, would simplify to 2 times s.

Negative 5 times negative 1 is plus 5.

Plus 5 is equal to 7, is equal to That was pretty straightforward. What we're going to do in this video is represent the same system, but we're going to represent it esssentially as a matrix equation, and we're going to solve it using inverse matrices.

I'll give you a little bit of a warning. It's going to be more involved. It's going to take us more time to this, and you're probably going to say, "Well, why are we even going through the trouble of it?

Maybe the left-hand sides are the same, the right-hands keep changing, and this might be something that you might see while writing a computer game or while working on some type of a computer problem. And this is a general theme. A lot of the value of matrices are they are ways to represent problems, mathematical problems, ways to represent data, and then we can use matrix operations, matrix equations to essentially manipulate them in appropriate ways if we're, for the most part, writing computer programs or things like computer programs.

Bear with me, you will enjoy it eventually, what we're about to do, and one day, you will see that it is actually quite useful. The first thing we need to see or need to appreciate is that this can be represented by a matrix equation. Now what I'm going to do is I'm going to take the coefficients here.

I'm going to take the coefficients here, so 2, negative 5, 2, negative 5, negative 2, negative 2 and 4, and positive 4. All I've done is I've taken the coefficients here, and I'm going to claim that that times the column vector, column vector st, s and t, being equal to the column vector 7, negative 6, 7, negative 6, is the exact same thing as what we have right over here.

These are representing the same constraints on the variable s and t.The word in square brackets is the alt text, which gets displayed if the browser can't show the image.

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Here is an example of some LaTeX code that will typeset a matrix. \left[ \begin {array}{ccc} 9&13&17\\ \noalign{\medskip} 14&18&22 \end {array} \right] If you put this code inside a LaTeX displaymath environment, you will get the matrix typeset.

Write LaTeX code to display the angle sum identity $$\cos(\alpha \pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta$$ Write LaTeX code to display the indefinite integral.

Once you build a body of custom commands that you will be using in many LaTeX documents, you should learn about creating your own package so you don't have to copy all your custom commands from document to document.

Matrices and other arrays in LaTeX. Matrices and other arrays are produced in LaTeX using the \textbf{array} environment. For example, suppose that we wish to typeset the following passage.

$\LaTeX$ macros for expectation, variance and covariance? - Cross Validated Meta