Let A=⎡⎢⎣100210321⎤⎥⎦. U1,U2,U3 are column matrices satisfying AU1=⎡⎢⎣100⎤⎥⎦, AU2=⎡⎢⎣230⎤⎥⎦ and AU3=⎡⎢⎣231⎤⎥⎦. If U is 3×3 matrix whose columns are U1,U2 and U3, then det(U) equals

Let A=⎡⎢⎣100210321⎤⎥⎦. U1,U2,U3 are column matrices satisf

1.	Let A=⎡⎢⎣100210321⎤⎥⎦. U1,U2,U3 are column matrices satisfying AU1=⎡⎢⎣100⎤⎥⎦, AU2=⎡⎢⎣230⎤⎥⎦ and AU3=⎡⎢⎣231⎤⎥⎦. If U is 3×3 matrix whose columns are U1,U2 and U3, then det(U) equals
Answer» Let $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦ .$ $U_{1}, U_{2}, U_{3}$ are column matrices satisfying $A U_{1} = ⎡ ⎢ ⎣ \begin{matrix} 100 \end{matrix} ⎤ ⎥ ⎦,$ $A U_{2} = ⎡ ⎢ ⎣ \begin{matrix} 230 \end{matrix} ⎤ ⎥ ⎦$ and $A U_{3} = ⎡ ⎢ ⎣ \begin{matrix} 231 \end{matrix} ⎤ ⎥ ⎦ .$ If $U$ is $3 \times 3$ matrix whose columns are $U_{1}, U_{2}$ and $U_{3},$ then $det (U)$ equals