数学试题讲解

求向量组

α_{1} = (\begin{array}{l} 1 \\ 1 \\ 2 \\ 3 \end{array}), α_{2} = (\begin{array}{l} 1 \\ - 1 \\ 1 \\ 1 \end{array}), α_{3} = (\begin{array}{l} 1 \\ 3 \\ 3 \\ 5 \end{array}), α_{4} = (\begin{array}{l} 4 \\ - 2 \\ 5 \\ 6 \end{array})

的秩和一个极大线性无关组,并把其余向量用极大线性无关组线性表出.