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weamp;#39;ve seen two different matrix decompositions the singular value decomposition and the QR decomposition what I want to do in this video is demonstrating how both of these are useful for solving systems of equations the fundamental problem is linear algebra is to solve the problem ax equals B you have a fixed matrix a and a fix matrix B and you want to find the x solve this linear system of equations thatamp;#39;s where it all begins now of course youamp;#39;d say well perhaps a has an inverse we can apply your operations to find a inverse and then x is a inverse B thatamp;#39;s certainly true as far as it goes but perhaps a inverses I exist but we still on two solutions say using some reduced row echelon form of a and their operations a pseudo inverse on their hand it turns out this operation of Denver operations is not exactly numerically stable if you have small errors an A or B they can accumulate to this process of of manipulation and division of the different rows and
