
The number of non- trivial solution of the system and is:
A) 0. B) 1. C) 2. D) 3
Answer
517.5k+ views
Hint: For the non- trivial solution for the system of equations. The determinant of the coefficient of the matrix is zero.
Complete step-by-step answer:
In the question given above, we are asked for the number of non- trivial solutions for the given equation.
The equation given in the question are as follows:
①
②
And ③
Now, if we are asked for the non-trivial solution for the given system of linear equations, then we find the determinant of the coefficient of the matrix which must be equal to zero (0).
So, coefficient of equation ①; of respectively are 1,-1, and 1 for similarly, the coefficient of equation ②; for respectively are for equation
In the similar manner,
the coefficient of equation ③; for respectively are for equation
finding determinant:
For determinant of ;
So,
So, here determinant value in 9 not 0
Hence, the given system of linear equations has no trivial solution.
Therefore the number of trivial solutions is 0.
Note : The given system of linear equations will have a non-trivial solution only if the determinant of the coefficient of the matrix is zero.
Complete step-by-step answer:
In the question given above, we are asked for the number of non- trivial solutions for the given equation.
The equation given in the question are as follows:
And
Now, if we are asked for the non-trivial solution for the given system of linear equations, then we find the determinant of the coefficient of the matrix which must be equal to zero (0).
So, coefficient of equation ①; of
In the similar manner,
the coefficient of equation ③; for
finding determinant:
For determinant of ;
So,
So, here determinant value in 9 not 0
Hence, the given system of linear equations has no trivial solution.
Therefore the number of trivial solutions is 0.
Note : The given system of linear equations will have a non-trivial solution only if the determinant of the coefficient of the matrix is zero.
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