A system of linear equations is called homogeneous if all of the constant terms are zero. The trivial solution is obtained by assigning the value of zero to each of the variables. a) Can a homogenous system of linear equations have no solutions? b) Find all the values of for which the following homogeneous system has a non-trivial solution (has infinitely many solutions). Find the general solution for x,y,z and in this case. x-2y+z=0 x+ay-3z=0 -x+6y-5z=0

cuuhorre76

cuuhorre76

Answered question

2022-09-05

A system of linear equations is called homogeneous if all of the constant terms are zero. The trivial solution is obtained by assigning the value of zero to each of the variables.
a) Can a homogenous system of linear equations have no solutions?
b) Find all the values of for which the following homogeneous system has a non-trivial solution (has infinitely many solutions). Find the general solution for x,y,z and in this case.
x-2y+z=0
x+ay-3z=0
-x+6y-5z=0

Answer & Explanation

Anabelle Guzman

Anabelle Guzman

Beginner2022-09-06Added 14 answers

a, No. It can only have a unique solution or infinitely many solutions
b, As long as a different than 2, the system has non trivial solution.

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