# Matrices may be long.

Algebra Level 3

If

$$A = \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \\ \end{bmatrix}$$

and $$U_1 , U_2$$ and $$U_3$$ are column matrices satisfying

$$AU_1 = \begin{bmatrix} 1 \\ 0 \\ 0 \\ \end{bmatrix}$$

$$AU_2 = \begin{bmatrix} 2 \\ 3 \\ 0 \\ \end{bmatrix}$$

$$AU_3 = \begin{bmatrix} 2 \\ 3 \\ 1 \\ \end{bmatrix}$$

and $$U$$ is a $$3 \times 3$$ matrix whose columns $$C_1 , C_2 , C_3$$ are $$U_1 , U_2 , U_3$$ respectively, then the value of $$|U|$$ is

×