Answer to Question #213092 in Linear Algebra for Dhruv bartwal

Question

A homogeneous system of linear equations has only the trivial solution.

True or false with full explanation

Answer 1

Homogeneous systems always have a solution and are therefore compatible. The special solution $(0,0,\ldots,0)$ is called trivial solution and is obtained by making all variables null. In some cases, they have only the trivial solution, and in others, infinite solutions in addition to the trivial one. This depends on whether the rank of the coefficient matrix coincides with the number of unknowns or not. If it matches, it has only the trivial solution; and if it does not match, it has infinite solutions.

Therefore, the expression is false.