GATE | GATE-CS-2005 | Question 48

Consider the following system of equations in three real variables xl, x2 and x3
2×1 – x2 + 3×3 = 1
3×1- 2×2 + 5×3 = 2
-x1 + 4×2 + x3 = 3
This system of equations has

(A) no solution
(B) a unique solution
(C) more than one but a finite number of solutions
(D) an infinite number of solutions


Answer: (B)

Explanation:

Consider the matrix as A

| A | = 2 ( 2 -20 ) +1 ( 3 + 5 ) + 3 ( 12 + 2 )

      = 36 + 8+ 42

     = 86

The determinant value of following matrix is non-zero, therefore we have a unique solution. 

 2   -1   3
 3   -2   5
-1    4   1  

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