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Illustrations in Jade Mirror of the Four Unknowns Jia Xian triangle. Jade Mirror of the Four Unknowns, [1] Siyuan yujian (simplified Chinese: 四元玉鉴; traditional Chinese: 四元玉鑒), also referred to as Jade Mirror of the Four Origins, [2] is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. [3]
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
[2] [3] [4] Using logarithmic tables, he calculated the first digits of the smallest solution, showing that it is about 7.76 × 10 206 544 cattle, far more than could fit in the observable universe. [5] The decimal form is too long for humans to calculate exactly, but multiple-precision arithmetic packages on computers can write it out explicitly.
An indeterminate system by definition is consistent, in the sense of having at least one solution. [3] For a system of linear equations, the number of equations in an indeterminate system could be the same as the number of unknowns, less than the number of unknowns (an underdetermined system), or greater than the number of unknowns (an ...
[4] [5] [6] Cramer's rule, implemented in a naive way, is computationally inefficient for systems of more than two or three equations. [7] In the case of n equations in n unknowns, it requires computation of n + 1 determinants, while Gaussian elimination produces the result with the same computational complexity as the computation of a single ...
The system + =, + = has exactly one solution: x = 1, y = 2 The nonlinear system + =, + = has the two solutions (x, y) = (1, 0) and (x, y) = (0, 1), while + + =, + + =, + + = has an infinite number of solutions because the third equation is the first equation plus twice the second one and hence contains no independent information; thus any value of z can be chosen and values of x and y can be ...
Uncertainty is sometimes classified into two categories, [8] [9] prominently seen in medical applications. [10]Aleatoric Aleatoric uncertainty is also known as stochastic uncertainty, and is representative of unknowns that differ each time we run the same experiment.
Substitute this expression into the remaining equations. This yields a system of equations with one fewer equation and unknown. Repeat steps 1 and 2 until the system is reduced to a single linear equation. Solve this equation, and then back-substitute until the entire solution is found. For example, consider the following system: