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Home  >>  CBSE XII  >>  Math  >>  Matrices
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If possible,find BA and AB,where\[A=\begin{bmatrix}2 & 1 & 2\\1 & 2 & 4\end{bmatrix},B=\begin{bmatrix}4 & 1\\2 & 3\\1 & 2\end{bmatrix}\]

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BA=$\begin{bmatrix}4 & 1\\2 & 3\\1 & 2\end{bmatrix}\begin{bmatrix}2 & 1 & 2\\1 & 2 & 4\end{bmatrix}$
 
$\;\;\;=\begin{bmatrix}4(2)+1(1) & 4(1)+1(2) & 4(2)+1(4)\\2(2)+3(1) & 2(1)+3(2) & 2(2)+3(4)\\1(2)+2(1) & 1(1)+2(2) & 1(2)+2(4)\end{bmatrix}$
 
$\;\;\;=\begin{bmatrix}8+1 & 4+2 & 8+4\\4+3 & 2+6 & 4+12\\2+2 & 1+4 & 2+8\end{bmatrix}$
 
$\;\;\;=\begin{bmatrix}9 & 6 & 12\\7 & 8 & 16\\4 & 5 & 10\end{bmatrix}$
 
AB=$\begin{bmatrix}2 & 1 & 2\\1 & 2 & 4\end{bmatrix}\begin{bmatrix}4 & 1\\2 & 3\\1 & 2\end{bmatrix}$
 
$\;\;\;=\begin{bmatrix}2(4)+1(2)+2(1) & 2(1)+1(3)+2(2) \\1(4)+2(2)+4(1) & 1(1)+2(3)+4(2) \end{bmatrix}$
 
$\;\;\;=\begin{bmatrix}8+2+2& 2+3+4 \\4+4+4 & 1+6+8 \end{bmatrix}$
 
$\;\;\;=\begin{bmatrix}12& 9 \\12 & 15 \end{bmatrix}$

 

answered Mar 5, 2013 by sreemathi.v
 

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