Let's talk about an extremely important application of vectors which is the linear combination , or linear combinations. In general, we have y equals and we might have a set of vectors here and they might be, let's call them V_1, V_2, all the way up to V_n. These individual VIs V_1, V_2, any of them, those are in and of themselves a column vector. We'll have one column vector and another column vector and they're all the same dimensions, meaning, of course, they're column vectors, so they only have one column. When I say the same dimension, I mean they have the same number of rows. In general, a linear combination of vectors is just a scalar, any numbers, some weight attached to it, times a vector plus a different weight or it can be the same weight but we're just considering them independent scalars here. So C_1, any scalar times V_1, which is again just a vector, plus C_2, which is pretty much any number times V_2, which is a different vector all the way up to C_n, which is a different number, again, can be the same number, but it's just some scalar times V_n. It's just a combination of some weight scalar, 2, 5, square root of 3, whatever, times a vector and then we add up all of those. In general, one example might be, let's say I have V_1 equals 0, 1, and I have V_2 equals negative 1, 3. One specific linear combination might be square root of 3 times 0, 1 plus 14 times negative 1, 3. I'm not sure why it took me so long to think of 14. But again, this is just some number times a vector plus some number times a vector and that's a linear combination. It's just a concept to understand in the beginning that again, it's just each vector out of a set of vectors multiplied by some number and we add them all together and that's the linear combination of that set of vectors. The next time we're going to do a specific example of this and see what you can get out of it.