xy + yz + zx = – 1
This homogeneous system of equations can’t have trivial solution i.e., as it will make x, y, z not defined.
Hence determinant of coefficients should be zero.
If a, b, c are the sides of a ΔABC opposite to angle A, B, C respectively, then
The value of lying between and satisfying the equation
has a non-zero solution, then value of
If a determinate of is formed by using the number 1 or –1 then minimum value of determinant is :
A and B are square matrices and A is non-singular matrix, :
The value of such that the system x – 2y + z = –4, 2x – y + 2z = 2, has no solution is :
The homogeneous system of equation :
has non-trivial solutions if :
then the number of solutions of the system of equations