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X + 5 y = 0
- A solution or example that is ridiculously simple and of little interest. Often, solutions or examples involving the number 0 are considered trivial. Nonzero solutions or examples are considered nontrivial. For example, the equation x + 5 y = 0 has the trivial solution x = 0, y = 0.
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Nov 8, 2016 · For example, for the homogeneous linear equation $7x+3y-10z=0$ it might be a trivial affair to find/verify that $(1,1,1)$ is a solution. But the term trivial solution is reserved exclusively for for the solution consisting of zero values for all the variables.
The trivial solution is the zero function. while a nontrivial solution is the exponential function. The differential equation with boundary conditions is important in mathematics and physics, as it could be used to describe a particle in a box in quantum mechanics, or a standing wave on a string.
Examples of Triviality. In linear algebra, let X be the unknown vector and A is the matrix and O is zero vector. One simple solution of matrix equation AX = O is X = 0 which is known as “trivial solution”. Any other non-zero solution is termed as a “non-trivial” solution. Let us assume that ‘n’ be an integer number.
Trivial. A solution or example that is ridiculously simple and of little interest. Often, solutions or examples involving the number 0 are considered trivial. Nonzero solutions or examples are considered nontrivial. For example, the equation x + 5y = 0 has the trivial solution x = 0, y = 0
Page ID. A system of equations in the variables x1, x2, …, xn is called homogeneous if all the constant terms are zero—that is, if each equation of the system has the form. a1x1 + a2x2 + ⋯ + anxn = 0. Clearly x1 = 0, x2 = 0, …, xn = 0 is a solution to such a system; it is called the trivial solution.
A homogeneous system of linear equations is a system in which each linear equation has no constant term. Learn how to find the trivial and nontrivial solutions of a homogeneous linear system along with many examples.
Sep 17, 2022 · Notice that if \(n=m\) or \(n<m\), it is possible to have either a unique solution (which will be the trivial solution) or infinitely many solutions. We are not limited to homogeneous systems of equations here. The rank of a matrix can be used to learn about the solutions of any system of linear equations.
