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. The value of inverse from the system of equations

            2x - y + 3z = 9,   x + y + z = 6, x - y + z = 2

Option: 1

\begin{bmatrix} -1 &1 &2 \\ 0&1/2 & -1/2\\ 1& -1/2 &-3/2 \end{bmatrix}


Option: 2

\begin{bmatrix} -1 & 1 &2 \\ 0& 1/2 &1/2\\ 1&-1/2 &3/2 \end{bmatrix}


Option: 3

\begin{bmatrix} -1 & 1 &2 \\ 0& 1/2 &1/2\\ 1&1/2 &-3/2 \end{bmatrix}


Option: 4

\begin{bmatrix} -1 & 1 &2 \\ 0&- 1/2 &1/2\\ 1&1/2 &-3/2 \end{bmatrix}


Answers (1)

best_answer

As we habe learned

System of simultaneous linear equation -

- wherein

The n\times n matrix A is called the coefficient matrix of the system of linear equation

 

 

The given system of equations can be written in matrix form as AX = B

            where A = \begin{bmatrix} 2 & -1 &3 \\ 1& 1 &1 \\ 1& -1 &1 \end{bmatrix}, X = \begin{bmatrix} x\\ y\\ z \end{bmatrix},        B = \begin{bmatrix} 9\\ 6\\ 2 \end{bmatrix}

We have |A| = -2 \neq  0 i.e. A is non - singular and therefore A-1 exists.

            We have A-1 = \frac{adjA}{\left | A \right |} = \begin{bmatrix} -1 &1 &2 \\ 0&1/2 &1/2 \\ 1& -1/2 &-3/2 \end{bmatrix}

Therefore X = A-1 B = \begin{bmatrix} -1 &1 &2 \\ 0 &1/2 &-1/2 \\ 1& -1/2 &-3/2 \end{bmatrix}\begin{bmatrix} 9\\ 6\\ 2 \end{bmatrix}

\Rightarrow X = \begin{bmatrix} x\\ y\\ z \end{bmatrix} = \begin{bmatrix} 1\\ 2\\ 3 \end{bmatrix}  i.e.(x, y, z) = (1, 2, 3)

 

Posted by

sudhir.kumar

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