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GATE 2022 AG – Question 37

Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice

For what listed values of x is $\begin{pmatrix}3-x&2&2\\2&4-x&1\\-2&-4&-1-x\end{pmatrix}$ singular?

  1. x=0 and x=3
  2. x=0 and x=−3
  3. x=0 and x=6
  4. x=0 and x=−6

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Correct answer: (A) x=0 and x=3

Explanation

Singularity means zero determinant. Expanding and factoring gives $-x(x-3)^2=0$. Therefore the values are **0 and 3, A**. The repeated root3 remains one distinct singular value; solving individual diagonal entries would not find the determinant roots.

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