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Home  >>  CBSE XII  >>  Math  >>  Model Papers
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Write the value of the determinants \[ \begin{vmatrix} 2 & 3 & 4 \\ 5 & 6 & 8 \\ 6x & 9x & 12x \end{vmatrix} \]

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Toolbox:
  • The Value of the determinant of a $3\times 3$ matrix can be obtained by\[\begin{bmatrix}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\a_{31}& a_{32} & a_{33}\end{bmatrix}\]
  • If two rows (or columns) are identical,the value of the determinant is 0.
  • $\Delta =a_{11}(a_{22}\times a_{33}-a_{23}\times a_{32})-a_{12}(a_{21}\times a_{33}-a_{23}\times a_{31})+a_{13}(a_{21}\times a_{32}-a_{22}\times a_{31})$
Given $\Delta=\begin{bmatrix}2 & 3 & 4\\5 & 6 & 8\\6x & 9x & 12x\end{bmatrix}$
 
Let $\Delta=\begin{bmatrix}2 & 3 & 4\\5 & 6 & 8\\6x&9x &12x\end{bmatrix}$
 
Let us take 3x which is the common factor of $R_3$,then
 
$\Delta=\begin{bmatrix}2 & 3 & 4\\5 & 6 & 8\\2 & 3 & 4\end{bmatrix}$
 
Since two rows are identical ,the value of the determinant is zero.
 
Hence $\Delta=0.$

 

answered Mar 11, 2013 by sreemathi.v
 

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