Home › MCQs › SSC Pure Mathematics › Question #1277
Back to Questions
SSC Pure Mathematics QUESTION #1277
Question 1
For the system of equations with parameter \(a\): \(x+2y-3z=4\), \(3x-y+5z=2\), \(4x+y+(a^2-14)z=a+2\), the system has infinitely many solutions when \(a\) equals:
  • 2
  • \(-2\)
  • Both \(2\) and \(-2\)✔️
  • No value of \(a\)
Correct Answer Explanation
Row-reducing the augmented matrix leads to the condition \((a^2-14-\text{something})z=a+2-\text{something}\). The coefficient of \(z\) in the last row becomes \(a^2-14+\frac{14}{7}\cdot...\). After elimination: \((a^2-4)z=(a-2)\) in the last equation. For infinite solutions: coefficient and RHS both zero: \(a^2-4=0\Rightarrow a=\pm2\) and \(a-2=0\Rightarrow a=2\). So infinite solutions at \(a=2\); no solution at \(a=-2\).