The number of solutions of equations x2-x3=1,-x1+ 2 x3=2, x1-2 x2=3 is (A) zero (B) one (C) two

step 1 Find the number of solutions of the equations x2 minus x3 equal to 1 minus x1 plus 2 x3 equal to

The number of solutions of equations x2-x3=1,-x1+ 2 x3=2,...

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations with a set of common variables. The goal is to find values for the variables that satisfy all equations simultaneously. This concept is fundamental in algebra and linear algebra, providing methods for modeling and solving problems in various fields including engineering, economics, and the sciences.

Consistency and Inconsistency

A system of linear equations is considered consistent if there exists at least one set of values for the variables that satisfies all equations; otherwise, it is classified as inconsistent. The analysis of consistency involves checking for contradictory equations, which can lead to no solution, a unique solution, or infinitely many solutions depending on the relationship between the equations.

Methods of Solving Linear Systems

Various methods can be employed to solve linear systems, including substitution, elimination, and matrix techniques like Gaussian elimination or using determinants. These methods help in systematically reducing the system to a simpler form, ultimately revealing whether the system is consistent or inconsistent and, if consistent, determining the nature of its solutions.

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