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Home  >>  CBSE XII  >>  Math  >>  Model Papers
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Write the order of the product matrix : $ \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \begin{bmatrix} 2 & 3 & 4 \end{bmatrix} $

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Toolbox:
  • Order of matrix$\rightarrow$ A matrix having m rows and n columns of the order $m\times n$
  • If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B: $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$
Given:
$\begin{bmatrix}1\\2\\3\end{bmatrix}\begin{bmatrix}2 & 3& 4\end{bmatrix}$
$\Rightarrow \begin{bmatrix}1\times 2 &1\times 3 & 1\times 4\\2\times 2&2\times 3& 2\times 4\\3\times 2&3\times 3&3\times 4\end{bmatrix}$
$\Rightarrow \begin{bmatrix}2 & 3& 4\\4 & 6 &8\\6 & 9& 12\end{bmatrix}$
The above given matrix has 3 rows and 3 columns.
Order of matrix$\Rightarrow 3\times 3$
answered Apr 8, 2013 by sharmaaparna1
 

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