数学试题讲解

设

A, P

均为 3 阶方阵,

P^{T}

为

P

的转置矩阵, 且

P^{T} A P = [\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2 \end{array}]

, 若

P =

(α_{1}, α_{2}, α_{3}), Q (α_{1} + α_{2}, α_{2}, α_{3})

, 则

Q^{T} A Q

为

[\begin{array}{lll} 1 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 2 \end{array}]

[\begin{array}{lll} 2 & 1 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 2 \end{array}]

[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2 \end{array}]

[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{array}]