The system of equations which can be solved by matrix inversion method have_______.

unique solution

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no solution

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infinitely many solutions

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two solutions

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Solution

The correct option is A unique solution
The system of equations which can be solved by matrix inversion method have a unique solution.

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⎛ ⎜ ⎝ \begin{matrix} 1 & 1 & 1 2 & 5 & 7 2 & 1 & - 1 \end{matrix} ⎤ ⎥ ⎦ ⎛ ⎜ ⎝ \begin{matrix} x_{1} & y_{1} x_{2} & y_{2} x_{3} & y_{3} \end{matrix} ⎤ ⎥ ⎦ = ⎛ ⎜ ⎝ \begin{matrix} 9 & 2 52 & 15 0 & - 1 \end{matrix} ⎤ ⎥ ⎦

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

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 2 & 5 & 7 2 & 1 & - 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} x_{1} & y_{1} x_{2} & y_{2} x_{3} & y_{3} \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 9 & 2 52 & 15 0 & - 1 \end{matrix} ⎤ ⎥ ⎦

x_{1} + y_{3}

2 x - y = 7; 3 x - 2 y = 11

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 2 & 5 & 7 2 & 1 & - 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} x & u y & v z & w \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 9 & 2 52 & 15 0 & - 1 \end{matrix} ⎤ ⎥ ⎦

x y z - u v w

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