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GATE Mechanical 2024 | Question: 4

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​​​​​Consider the system of linear equations

\[
\begin{array}{c}
x+2 y+z=5 \\
2 x+a y+4 z=12 \\
2 x+4 y+6 z=b
\end{array}
\]

The values of $a$ and $b$ such that there exists a non-trivial null space and the system admits infinite solutions are

  1. $a=8, b=14$
  2. $a=4, b=12$
  3. $a=8, b=12$
  4. $a=4, b=14$

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