Question

Let a,b,c be positive real numbers. The following system of equations in x,y,z

$\frac{x^2}{a^2}-\frac{y^2}{b^2}-\frac{z^2}{c^2}=1,-\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1,-\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

• A. No solution
• B. unique solution
• C. infinitely many solutions
• D. finitely many solutions

Answer 1

The correct option is

D

Since, we know if determinant of the matrix corresponding to the given linear system is not zero then system has unique solution.

So, at first we find the determinant of the given system.

Matrix corresponding to given system define as-

Hence, given system has a unique solution.​