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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