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Let a, b, c be positive real numbers. Th...

Let a, b, c be positive real numbers. The following system of equations in x,y and z
`(x^(2))/(a^(2)) = (y^(2))/(b^(2)) - (z^(2))/(c^(2)) = 1, (x^(2))/(a^(2)) - (y^(2))/(b^(2)) + (z^(2))/(c^(2)) = 1, - (x^(2))/(a^(2)) + (y^(2))/(b^(2)) + (z^(2))/(c^(2)) = 1` has

A

infinite solutions

B

unique solution

C

no solution

D

finite number of solutions.

Text Solution

Verified by Experts

The correct Answer is:
B
Let `(x^(2))/(a^(2))=X,(y^(2))/(b^(2))=Y` and `(z^(2))/(c^(2))=Z` then the given equation will be
`X+Y-Z=1`,
`X-Y+Z=1`,
`-X+Y+Z=1`
It can be written in matrix form as `AX=B`
Here `A=[(1,1,-1),(1,-1,1),(-1,1,1)]`
Now `|A|=1(-1-1)-(1+1)-1(1-1)=-4!=0`
Therefore, the given system of equation has unique solution.
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