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In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...
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]
The Book of Computations is the first known text to solve systems of equations with two unknowns. [20] There are a total of three sets of problems within The Book of Computations involving solving systems of equations with the false position method, which again are put into practical terms. [20]
with unknowns x, y and z, can be put in the above form by subtracting 21z from both sides of the equation, to obtain 3 x + 2 y − 21 z = 0 {\displaystyle 3x+2y-21z=0} In this particular case there is not just one solution, but an infinite set of solutions, which can be written using set builder notation as
This counterintuitive result occurs because in the case where =, multiplying both sides by multiplies both sides by zero, and so necessarily produces a true equation just as in the first example. In general, whenever we multiply both sides of an equation by an expression involving variables, we introduce extraneous solutions wherever that ...
Functional equation – equation in which the unknowns are functions rather than simple quantities. Differential equation – equation involving derivatives. Integral equation – equation involving integrals. Diophantine equation – equation where the only solutions of interest of the unknowns are the integer ones.
In this case, the unique solution is described by a sequence of equations whose left-hand sides are the names of the unknowns and right-hand sides are the corresponding values, for example (=, =, =). When an order on the unknowns has been fixed, for example the alphabetical order the solution may be described as a vector of values, like ( 3 ...
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