GATE | GATE-CS-2005 | Question 48

Consider the following system of equations in three real variables x₁, x₂ and x₃

2x1 - x2 + 3x3 = 1 
3x1- 2x2 + 5x3 = 2
-x1 + 4x2 + 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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