GATE 2014 CS (CS2) – Question 14
If $A=\begin{pmatrix}2\\-4\\7\end{pmatrix}\begin{pmatrix}1&9&5\end{pmatrix}$, find det(A).
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Correct answer: 0 to 0
Explanation
The3by3matrix is the outer product of one column and one row. Every column is a scalar multiple of the same column vector, so its rank is at most1. It is singular and its determinant is **0**. Expanding all nine entries is unnecessary.