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A system of m linear algebraic equations

Lecture





The system of m linear equations:

a m 1 x 1 + a m 2 x 2 + ... + a m n x n = b m , m = 1, 2, ..., n.

A system of n linear equations with n unknowns can be rewritten as:

  A system of m linear algebraic equations

where a 11 , a 12 , ..., and nn are coefficients, b 1 , b 2 , ..., b n are free members and x 1 , x 2 , ..., x n are unknown.

The set of n numbers x 1 , ..., x n , which, being substituted into the original system, turn equations into identities, is called a solution of the system. A system that has at least one solution is called a joint. A system that does not have a solution at all is called incompatible.

Cramer's Rule

If the determinant of the system is nonzero

  A system of m linear algebraic equations

the system has the only solution sought by Cramer’s rule:

  A system of m linear algebraic equations

where det k is the determinant obtained by replacing the kth column of the original determinant of the system by the column of free terms:

  A system of m linear algebraic equations

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HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS

Terms: HANDBOOK ON MATHEMATICS, SCHOOL MATHEMATICS, HIGHER MATHEMATICS