سِڌِر مساواتُن جو سرشتو: جي ورجائن ۾ تفاوت

Further, Cramer's rule has very poor numerical properties, making it unsuitable for solving even small systems reliably, unless the operations are performed in rational arithmetic with unbounded precision.

 

While systems of three or four equations can be readily solved by hand, computers are often used for larger systems. The standard algorithm for solving a system of linear equations is based on Gaussian elimination with some modifications. Firstly, it is essential to avoid division by small numbers, which may lead to inaccurate results. This can be done by reordering the equations if necessary, a process known as ''pivoting''. Secondly, the algorithm does not exactly do Gaussian elimination, but it computes the [[LU decomposition]] of the matrix ''A''. This is mostly an organizational tool, but it is much quicker if one has to solve several systems with the same matrix ''A'' but different vectors '''b'''.