数学试题讲解

设

α_{1}, α_{2}, α_{3}

是 3 维向量空间

R^{3}

的一组基, 则由基

α_{1}, \frac{1}{2} α_{2}, \frac{1}{3} α_{3}

到基

α_{1} + α_{2}, α_{2} + α_{3}, α_{3} + α_{1}

的过渡矩阵为

(\begin{array}{lll} 1 & 0 & 1 \\ 2 & 2 & 0 \\ 0 & 3 & 3 \end{array})

. B.

(\begin{array}{lll} 1 & 2 & 0 \\ 0 & 2 & 3 \\ 1 & 0 & 3 \end{array})

. C.

(\begin{array}{ccc} \frac{1}{2} & \frac{1}{4} & - \frac{1}{6} \\ - \frac{1}{2} & \frac{1}{4} & \frac{1}{6} \\ \frac{1}{2} & - \frac{1}{4} & \frac{1}{6} \end{array})

. D.

(\begin{array}{ccc} \frac{1}{2} & - \frac{1}{2} & \frac{1}{2} \\ \frac{1}{4} & \frac{1}{4} & - \frac{1}{4} \\ - \frac{1}{6} & \frac{1}{6} & \frac{1}{6} \end{array})