
The number of non- trivial solution of the system and is:
A) 0. B) 1. C) 2. D) 3
Answer
512.4k+ 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.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
Which one is a true fish A Jellyfish B Starfish C Dogfish class 11 biology CBSE

State and prove Bernoullis theorem class 11 physics CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells
