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GATE 2016 CE (CE2) – Question 36

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 2 marks · Multiple choice

The linear system $x+2y-3z=a$, $2x+3y+3z=b$, $5x+9y-6z=c$ is consistent if ______.

  1. $7a-b-c=0$
  2. $3a+b-c=0$
  3. $3a-b+c=0$
  4. $7a-b+c=0$

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Correct answer: (B) $3a+b-c=0$

Explanation

Three times the first coefficient row plus the second gives the third:3(1,2,−3)+(2,3,3)=(5,9,−6). The right sides must obey the same dependence for consistency. Thus c=3a+b, or **3a+b−c=0, B**. Otherwise elimination yields0 equal to a nonzero constant.