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Home  >>  CBSE XII  >>  Math  >>  Matrices
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Compute the indicated products: $(v)\;\begin{bmatrix}2 & 1\\3 & 2\\-1 & 1\end{bmatrix}\begin{bmatrix}1 & 0 &1\\-1 & 2 & 1\end{bmatrix}$

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Toolbox:
  • Multiplication of two matrices is defined only if the number of columns of the left matrix is the same as the number of rows of the right matrix.
  • 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:
  • $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$
$\begin{bmatrix}2 & 1\\3 & 2\\-1 & 1\end{bmatrix}\begin{bmatrix}1 & 0 &1\\-1 & 2 & 1\end{bmatrix} = \begin{bmatrix}2\times 1+1\times -1 & 2\times 0+1\times 2 & 2\times 1+1\times 1\\3\times 1+2\times -1 & 3\times -0+2\times 2+ & 3\times 1+2\times 1\\-1\times 1+1\times -1 & -1\times 0+1\times 2+ & -1\times 1+1\times 1\end{bmatrix}$
$\begin{bmatrix}2 & 1\\3 & 2\\-1 & 1\end{bmatrix}\begin{bmatrix}1 & 0 &1\\-1 & 2 & 1\end{bmatrix} = \begin{bmatrix}2-1 & 0+2 & 2+1\\3-2 & 0+4 & 3+2\\-1-1 & 0+2 & -1+1\end{bmatrix}$
$\begin{bmatrix}2 & 1\\3 & 2\\-1 & 1\end{bmatrix}\begin{bmatrix}1 & 0 &1\\-1 & 2 & 1\end{bmatrix} = \begin{bmatrix}1 & 2 & 3\\1 & 4 & 5\\-2 & 2 & 0\end{bmatrix}$
answered Feb 27, 2013 by balaji.thirumalai
 

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