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what should be the dimension of matrix to be multiplied with a $4\times 1$ matrix so that i can get a $2 \times 1$ matrix ?

To make it clear: $\left(\fbox{?}\times\fbox{?}\right)\left(4\times 1\right) = 2\times 1$.

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    The result of multiplying an $n\times p$ matrix by a $p\times m$ matrix is an $n\times m$ matrix.2012-03-05

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