The zero, one vector because it doesn't go atĪll in the X direction. Here, what would we call that? Well that we would call In the vertical direction or the Y direction, so this ![]() And then the bottom number, the zero is what we're doing Vertically like this the convention is that the top number here is what we're doing in the X direction. Vector like this, one, zero, when you write a vector So the first conceptual idea is that any point on our coordinate plane here and this of course is our XĪxis and this is our Y axis, can be represented by aĬombination of two vectors. So let's just start with some examples or some conceptual ideas. Video, we're going to explore how a two by two matrix can be interpreted as representing a transformation Therefore, it is important to use the correct matrix-vector multiplication format depending on how the coordinates of the points are represented. In this case, the dot product of a row of the matrix with the row vector would yield a scalar, not a vector. On the other hand, if the point's coordinates are represented as a 1 by 2 matrix (i.e., a row vector), the matrix-vector multiplication cannot be interpreted as a weighted sum in the same way. This is because each entry in the resulting vector is obtained by taking the dot product of a row of the matrix with the column vector, which is equivalent to a weighted sum of the components of the vector. ![]() When representing a point's coordinates as a 2 by 1 matrix (i.e., a column vector), the matrix-vector multiplication can be interpreted as a weighted sum of the components of the vector, where the weights are the entries of the matrix. In linear algebra, a linear transformation can be represented as a matrix-vector multiplication, where the matrix represents the transformation and the vector represents the coordinates of the point being transformed.
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