The system of equations x+y+z=2,3x−y+2z=6 and 3x+y+z=−18 has
A
A unique solution
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B
No solutions
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C
An infinite number of solutions
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D
Zero solution as the only solution
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Solution
The correct option is A A unique solution Given system of equation can be written as ⎡⎢⎣1113−12311⎤⎥⎦⎡⎢⎣xyz⎤⎥⎦=⎡⎢⎣26−18⎤⎥⎦ On solving the above system we get the unique solution x = -10, y = -4, z = 16.