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Home  >>  CBSE XII  >>  Math  >>  Determinants
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Examine the consistency of the system of equations:\[\] \[\quad 2x -y = 5 \] \[\quad x + y = 4\]

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Toolbox:
  • (i)A matrix is said to be invertible if inverse exists.
  • (ii)If A is a non singular matrix such that
  • AX=B
  • then X=$A^{-1}B$
  • using this we can solve system of equations,which has unique solutions.
The given system of equation is
 
2x-y=5
 
x+y=4
 
This can be written in the form AX=B,
 
$A=\begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\;X=\begin{bmatrix}x\\y\end{bmatrix}\;B=\begin{bmatrix}5\\4\end{bmatrix}$
 
Hence $\begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}5\\4\end{bmatrix}$
 
Now let us find the value of the determinant
 
|A|=2-(-1)=2+1=3$\neq 0$
 
Hence A is non-singular.
 
Therefore $A^{-1}$ exists.
 
Hence the given system is consistent.

 

answered Feb 26, 2013 by sreemathi.v
edited Feb 27, 2013 by vijayalakshmi_ramakrishnans
 

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