数学试题讲解

设

α_{1}, α_{2}, α_{3}

是三维向量空间

R^{3}

的基, 则由基

α_{1}, α_{2}, 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 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \end{array}]

[\begin{array}{lll} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}]

[\begin{array}{lll} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 1 \end{array}]

[\begin{array}{lll} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}]