Technically, though, we don't know if this function is continuous or if it is defined by that table and only has those 5 points. A quadratic describes the points that make a parabola. So, in each case shown in the table, y = x² + 10 and that is definitely a quadratic. Because it's very hard to drawĪ 4, 5, or 20 dimensional arrow like this.In Sal's table, notice that every value of y equals 10 plus x^2 In four dimensions itīecomes more abstract. And as we study moreĪnd more linear algebra, we're going to start extending And you'll see because this isĪ 3, 4, 5 triangle, that this actually has a magnitude of 5.
Pythagorean theorem to figure out the actual So this vector mightīe specified as 3, 4. Start at the end of the arrow and go to the front of it. Up and how much we're moving to the right when we Literally thinking about how much we're moving
It's shifting three in the horizontal direction,Īnd it's shifting positive four in the vertical direction. You were to break it down, in the horizontal direction, The first coordinate represents how much we're moving You might also see notation, andĪctually in the linear algebra context, it's more This one only moves in the horizontal dimension. In each of these dimensions? So for example, Numbers that tell you how much is this vector moving If you're in two dimensions, to specify two Like you can really operate on that easily. It in your notebook, you would typically put a If you're publishing aīook, you can bold it. Represent a vector, is usually a lowercase letter. It with a little bit more mathematical notation? So we don't have to So for example, this wouldīe the exact same vector, or be equivalent vector to this. Not care where we start, where we place it when we thinkĪbout it visually like this. Now, what's interestingĪbout vectors is that we only care about the magnitude West, that would be north, and then that would be south. Horizontal axis is say east, or the positive horizontalĭirection is moving in the east, this would be So for example, I could startĪn arrow right over here.
To the right, where we'll say the right is east. Our straight traditional two-dimensional vector We can mathematically deal with beyond three And then even four, five, six,Īs made dimensions as we want. Magnitude, 5 miles per hour, and the direction east. And now we wouldn'tĬall it speed anymore. Miles per are due east, this is a vector quantity. So for example,ĥ miles per hour due east. Vector, we would also have to specify the direction.
This is considered toīe a scalar quantity. Here, which is often referred to as a speed, is not a It's only specifyingĭirection this thing is moving 5 miles per hour in. This information by itself is not a vector quantity. You that something is moving at 5 miles per hour, Of what wouldn't and what would be a vector.
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