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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. – Arturo Magidin Mar 5 '12 at 19:19

When you multiply an $m$ x $n$ matrix by a $n$ x $p$ matrix, you get a $m$ x $p$ matrix.

So if $B$ is 4 x 1 and $C$ is 2 x 1, you want $A$ to be 2 x 4 in the equation $AB = C$.

Note that if your multiplication is the other way around (i.e. $A$ is 4 x 1, $C$ is 2 x 1, and you want a $B$ such that $AB = C$), there is no matrix that works.

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