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if \( \begin{bmatrix} x+2 & 3 \\ x+5 & 4 \end{bmatrix}=3,\) find the value of x.

1 Answer

Toolbox:
  • If $A=\begin{bmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{bmatrix}$then,
  • |A|=$a_{11}\times a_{22}-a_{12}\times a_{21}$
Given:
 
$\begin{vmatrix}x+2 & 3\\x+5 & 4\end{vmatrix}$=3.
 
On expanding we get,
 
$\Delta=4(x+2)-3(x+5)=3.$
 
$\Rightarrow 4x+8-3x-15=3.$
 
$\Rightarrow x-7=3.$
 
$\Rightarrow x=10.$
 
Hence x=10.

 

answered Mar 11, 2013 by sreemathi.v
 

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