Question

The homogeneous system of equation :

 has non-trivial solutions if :

Solution

Correct option is

For any abcd

Let A = 

   

Hence AX = 0 is the given homogeneous equation.

For non-trivial solutions,     

Hence, lets find the determinant of A  

    

            

Hence |A| = 0 for any abcd.     

  Non-trivial solutions exist for any value of abcd.  

SIMILAR QUESTIONS

Q1

 represent the sides of a triangleABC, then  is equal to :

Q2

  

    :

Q3

If abc are the sides of a ΔABC opposite to angle ABC respectively, then

                             :

Q4

The value of  lying between  and satisfying the equation  

        :

Q5

 

          .

          

            

has a non-zero solution, then value of  

         

Q6

If a determinate of  is formed by using the number 1 or –1 then minimum value of determinant is :

Q7

A and B are square matrices and A is non-singular matrix,  : 

Q8

 is :

Q9

The value of  such that the system x – 2y + z = –4, 2x – y + 2z = 2,  has no solution is : 

Q10

 :