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In the last video, along with the ideas of vector addition and scalar multiplication, I described vector coordinates, where thereamp;#39;s this back and forth between, for example, pairs of numbers and two-dimensional vectors. Now, I imagine the vector coordinates were already familiar to a lot of you, but thereamp;#39;s another kind of interesting way to think about these coordinates, which is pretty central to linear algebra. When you have a pair of numbers thatamp;#39;s meant to describe a vector, like 3, negative 2, I want you to think about each coordinate as a scalar, meaning, think about how each one stretches or squishes vectors. In the xy coordinate system, there are two very special vectors, the one pointing to the right with length 1, commonly called i-hat, or the unit vector in the x direction, and the one pointing straight up with length 1, commonly called j-hat, or the unit vector in the y direction. Now, think of the x coordinate of our vector as a scalar that scales
