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1. （解答题）在

R^{3}

中有两组基．

ξ_{1} = (\begin{array}{l} 1 \\ 0 \\ 1 \end{array}), ξ_{2} = (\begin{array}{l} 0 \\ 1 \\ 0 \end{array}), ξ_{3} = (\begin{array}{l} 1 \\ 2 \\ 2 \end{array}) .

η_{1} = (\begin{array}{l} 1 \\ 0 \\ 0 \end{array}), η_{2} = (\begin{array}{l} 1 \\ 1 \\ 0 \end{array}), η_{3} = (\begin{array}{l} 1 \\ 1 \\ 1 \end{array}) .

求：（1）由基

ξ_{1}, ξ_{2}, ξ_{3}

到基

η_{1}, η_{2}, η_{3}

的过渡矩阵；
（2）求

α = (1, 3, 0)^{T}

．在

ξ_{1}, ξ_{2}, ξ_{3}

和

η_{1}, η_{2}, η_{3}

下的坐标．