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  • Solve the following system of equations by matrix method : <img alt="2x - y + 3z = 12" src="https://learn.careers360.

Solve the following system of equations by matrix method :

x - y + 2z = 7

2x - y + 3z = 12

3x + 2y - z = 5

 

 

 
 
 
 
 

Answers (1)

Given : system of linear equations

x - y + 2z = 7

2x - y + 3z = 12

3x + 2y - z = 5

Given system of linear equations can be written in matrix form as  

\mathrm{AX}=\mathrm{B}\\

Where 

A = \left[\begin{array}{ccc} 1 & -1 & 2 \\ 2 & -1 & 3 \\ 3 & 2 & -1 \end{array}\right], X= \left[\begin{array}{l} x \\ y \\ z \end{array}\right], B=\left[\begin{array}{c} 7 \\ 12 \\ 5 \end{array}\right]\\

|\mathrm{A}|=-2 \neq 0\Rightarrow A $ is invertible

Adj A =\left[\begin{array}{ccc} -5 & 11 & 7 \\ 3 & -7 & -5 \\ -1 & 1 & 1 \end{array}\right]^T\\

A^{-1}=\frac{Adj A}{|A|}

A^{-1}=\frac{1}{-2}\left[\begin{array}{ccc} -5 & 3 & -1 \\ 11 & -7 & 1 \\ 7 & -5 & 1 \end{array}\right]\\

X=A^{-1} B

X=\frac{1}{-2}\left[\begin{array}{ccc} -5 & 3 & -1 \\ 11 & -7 & 1 \\ 7 & -5 & 1 \end{array}\right]\left[\begin{array}{c} 7 \\ 12 \\ 5 \end{array}\right]

X=\left[\begin{array}{l} 2 \\ 1 \\ 3 \end{array}\right]\\

x=2, y=1, z=3

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Safeer PP

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