向量组的线性表示设向量组α1=(-1,4,1),α2=(-2,5,1),α3=(a,10,2),β=(1,c,b).当a,b,c满足什么条件时(1)β不能由α1,α2,α3线性表示(2)β能由α1,α2,α3线性表示,但表示不唯一,并写出一般的表达式.
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![向量组的线性表示设向量组α1=(-1,4,1),α2=(-2,5,1),α3=(a,10,2),β=(1,c,b).当a,b,c满足什么条件时(1)β不能由α1,α2,α3线性表示(2)β能由α1,α2,α3线性表示,但表示不唯一,并写出一般的表达式.](/uploads/image/z/5166480-48-0.jpg?t=%E5%90%91%E9%87%8F%E7%BB%84%E7%9A%84%E7%BA%BF%E6%80%A7%E8%A1%A8%E7%A4%BA%E8%AE%BE%E5%90%91%E9%87%8F%E7%BB%84%CE%B11%3D%28-1%2C4%2C1%29%2C%CE%B12%3D%28-2%2C5%2C1%29%2C%CE%B13%3D%28a%2C10%2C2%29%2C%CE%B2%3D%281%2Cc%2Cb%29.%E5%BD%93a%2Cb%2Cc%E6%BB%A1%E8%B6%B3%E4%BB%80%E4%B9%88%E6%9D%A1%E4%BB%B6%E6%97%B6%EF%BC%881%EF%BC%89%CE%B2%E4%B8%8D%E8%83%BD%E7%94%B1%CE%B11%2C%CE%B12%2C%CE%B13%E7%BA%BF%E6%80%A7%E8%A1%A8%E7%A4%BA%EF%BC%882%EF%BC%89%CE%B2%E8%83%BD%E7%94%B1%CE%B11%2C%CE%B12%2C%CE%B13%E7%BA%BF%E6%80%A7%E8%A1%A8%E7%A4%BA%2C%E4%BD%86%E8%A1%A8%E7%A4%BA%E4%B8%8D%E5%94%AF%E4%B8%80%2C%E5%B9%B6%E5%86%99%E5%87%BA%E4%B8%80%E8%88%AC%E7%9A%84%E8%A1%A8%E8%BE%BE%E5%BC%8F.)
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