Suppose the vectors X1, X2 and X3 are the solutions of the system of linear equations, Ax=b when the vector b on the right side is equal to b1, b2 and b3 respectively. ifX1=⎡⎢⎣111⎤⎥⎦, X2=⎡⎢⎣021⎤⎥⎦, X3=⎡⎢⎣001⎤⎥⎦, b1=⎡⎢⎣100⎤⎥⎦, b2=⎡⎢⎣020⎤⎥⎦ and b3=⎡⎢⎣002⎤⎥⎦, then the determinant of A is equal to

Suppose the vectors X1, X2 and X3 are the solutions of the system of l

1.	Suppose the vectors X1, X2 and X3 are the solutions of the system of linear equations, Ax=b when the vector b on the right side is equal to b1, b2 and b3 respectively. ifX1=⎡⎢⎣111⎤⎥⎦, X2=⎡⎢⎣021⎤⎥⎦, X3=⎡⎢⎣001⎤⎥⎦, b1=⎡⎢⎣100⎤⎥⎦, b2=⎡⎢⎣020⎤⎥⎦ and b3=⎡⎢⎣002⎤⎥⎦, then the determinant of A is equal to
Answer» Suppose the vectors $X_{1}$ , $X_{2}$ and $X_{3}$ are the solutions of the system of linear equations, $A x = b$ when the vector $b$ on the right side is equal to $b_{1}$ , $b_{2}$ and $b_{3}$ respectively. if $X_{1} = ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦, X_{2} = ⎡ ⎢ ⎣ \begin{matrix} 021 \end{matrix} ⎤ ⎥ ⎦, X_{3} = ⎡ ⎢ ⎣ \begin{matrix} 001 \end{matrix} ⎤ ⎥ ⎦, b_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦, b_{2} = ⎡ ⎢ ⎣ \begin{matrix} 020 \end{matrix} ⎤ ⎥ ⎦$ and $b_{3} = ⎡ ⎢ ⎣ \begin{matrix} 002 \end{matrix} ⎤ ⎥ ⎦$ , then the determinant of $A$ is equal to