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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 ...
When the solution set is finite, it is reduced to a single element. 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 (=, =, =).
Cramer's rule: In linear algebra, 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. Named after Swiss mathematician Gabriel Cramer .
Cramer's rule is a closed-form expression, in terms of determinants, of the solution of a system of n linear equations in n unknowns. Cramer's rule is useful for reasoning about the solution, but, except for n = 2 or 3, it is rarely used for computing a solution, since Gaussian elimination is a faster algorithm.
Cramer was born on 31 July 1704 in Geneva, Republic of Geneva to Jean-Isaac Cramer, a physician, and Anne Mallet. [1] The progenitor of the Cramer family in Geneva was Jean-Ulrich Cramer, Gabriel's great-grandfather, who immigrated from Strasbourg in 1634. [2] Cramer's mother, a member of the Mallet family, was of Huguenot origin. [3]
Consider the system of equations x + y + 2z = 3, x + y + z = 1, 2x + 2y + 2z = 2.. The coefficient matrix is = [], and the augmented matrix is (|) = [].Since both of these have the same rank, namely 2, there exists at least one solution; and since their rank is less than the number of unknowns, the latter being 3, there are infinitely many solutions.
The conclusion of the two meta-analyses and the systematic reviews, and the overall conclusion of the most recent scholarly work on SFBT, is that solution-focused brief therapy is an effective approach to the treatment of psychological problems, with effect sizes similar to other evidenced-based approaches, such as CBT and IPT, but that these ...
Human Givens therapy is a solution-focused brief therapy, [30] an approach that is aligned with solution-focused coaching and wellness coaching, [31] and thus the Human Givens approach is used by psychotherapists as well as life coaches [32] [33] and therapeutic coaches.