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GATE 2018 CE (CE1) – Question 11

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice

Which matrix is singular?

  1. $$\begin{bmatrix}2&5\\1&3\end{bmatrix}$$
  2. $$\begin{bmatrix}3&2\\2&3\end{bmatrix}$$
  3. $$\begin{bmatrix}2&4\\3&6\end{bmatrix}$$
  4. $$\begin{bmatrix}4&3\\6&2\end{bmatrix}$$

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Correct answer: (C) $$\begin{bmatrix}2&4\\3&6\end{bmatrix}$$

Explanation

A 2×2 matrix is singular when its determinant is zero. The four determinants are $6-5=1$, $9-4=5$, $12-12=0$ and $8-18=-10$. Thus C is singular.