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Showing how ANY linear transformation can be represented as a matrix vector product Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/linear_transformations/v/image-of-a-subset-under-a-transformation?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Missed the previous lesson? https://www ...
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Matrix transformations change the position, orientation, or size of vectors in space using multiplication. The matrix (0, 1.5, 1.5, 0) swaps the x and y components of any vector and scales them by 1.5. This means if you input a vector like (1, 2), the output would be (3, 1.5). Geometrically, this matrix reflects points across the line y = x and stretches them. It doesn’t preserve angles or lengths, but it keeps the origin fixed and turns lines into other lines, which is a key property of linear
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