数学试题讲解

设

A, P

均为 3 阶矩阵，

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} 2 & 1 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 2 \end{array})

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