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TIFR-2012-Maths-D: 36

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True/False Question:

The $10 \times 10 $ matrix $\begin{pmatrix} v_{1}w_{1} & \cdots&v_{1}w_{10} \\ v_{2}w_{2}& \cdots & v_{2}w_{10}\\ v_{10}w_{1}&\cdots & v_{10}w_{10} \end{pmatrix}$has rank $2$, where $v_{i},w_{i}\in \mathbb{C}.$

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