Bioengineering Industrial engineering With so much potential for specialization, many students want to know what courses they will need to take in high school to prepare for a successful start in college engineering classes. Four years of intensive language arts Four years of math including algebra II, geometry, trigonometry, and calculus Three years of science including biology, chemistry, and physics Two to three years of a foreign language Three years of social studies Two years of arts or humanities Computer Science It is best to take the highest possible level of these courses; for example, AP biology, AP computer science and so forth to prepare for the rigor of an engineering curriculum. Image courtesy of sxc.

Matrix dimensions Video transcript What I want to do in this video is explore the notion of a matrix outside of the context of a surprisingly good movie that involves Keanu Reeves. And it's actually the first of three. I guess we could call the three movies combined The Matrices. And there is a relationship between the movie, which is about a virtual reality constructed by super-smart computers, and the notion of what a matrix is when you study it in mathematics, or when you study it in computer science.

And the connection really is that matrices are used a lot when you are simulating things or when you're constructing things in computer science, especially in, frankly, computer graphics. So the super-intelligent robots that made the matrix in the movie Matrix were probably using matrices in order to do it, if they actually did exist.

Now, what is a matrix then?

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Well, that's a fairly simple answer. It's just a rectangular array of numbers.

So for Intro to engineering math, this right over here. If I have 1, 0, negative 7, pi, 5, and-- I don't know-- 11, this is a matrix. This is a matrix where 1, 0, negative 7, pi-- each of those are an entry in the matrix. This matrix right over here has two rows.

And it has three columns. And because it has two rows and three columns, people will often say that this is a 2 by 3 matrix. Whenever they say it's something by something matrix, they're telling you that it has two rows-- so you see the two rows right over there.

And they are telling you that it has three columns. You see the three columns right over there.

I could give you other examples of a matrix. So I could have a 1 by 1 matrix. So I could have the matrix 1. This right over here is a 1 by 1 matrix. It has one row, one column. I could have a matrix like this-- 3, 7, and Well, this has one row.

This is the one row that we see here. This is a 1 by 3 matrix. I could have a matrix-- and I think you see where all of this is going.

Figuring out the dimensions of a matrix are not too difficult. I could have a matrix that looks like this, where it's 3, 5, 0, 0, negative 1, negative 7.

This right over here has three rows. So it's three rows, and it has two columns. So we would call this a 3 by 2.

Let me do that in that same color. We would call it a 3 by 2 matrix, three rows and two columns. You know that a matrix is just a rectangular array of numbers. You can say what its dimensions are. You know that each of these numbers that take one of these positions-- we just call those entries.

But what are matrices good for? I still might not be clear what the connection is between this and this right over here. And at the most fundamental level, this is just a compact representation of a bunch of numbers.Buy Introduction to Engineering Mathematics 01 by Dr Anthony Croft, Robert Davison, Martin Hargreaves (ISBN: ) from Amazon's Book Store.

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