设3*3的矩阵A=(a.b.c),B=(d.b.c),其中a b c d均为三维列向量,已知行列式/A/=2,/B/=1\2,则行列式/A+2B/=?
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![设3*3的矩阵A=(a.b.c),B=(d.b.c),其中a b c d均为三维列向量,已知行列式/A/=2,/B/=1\2,则行列式/A+2B/=?](/uploads/image/z/5389102-46-2.jpg?t=%E8%AE%BE3%2A3%E7%9A%84%E7%9F%A9%E9%98%B5A%3D%28a.b.c%29%2CB%3D%28d.b.c%29%2C%E5%85%B6%E4%B8%ADa+b+c+d%E5%9D%87%E4%B8%BA%E4%B8%89%E7%BB%B4%E5%88%97%E5%90%91%E9%87%8F%2C%E5%B7%B2%E7%9F%A5%E8%A1%8C%E5%88%97%E5%BC%8F%2FA%2F%3D2%2C%2FB%2F%3D1%5C2%2C%E5%88%99%E8%A1%8C%E5%88%97%E5%BC%8F%2FA%2B2B%2F%3D%3F)
设3*3的矩阵A=(a.b.c),B=(d.b.c),其中a b c d均为三维列向量,已知行列式/A/=2,/B/=1\2,则行列式/A+2B/=?
设3*3的矩阵A=(a.b.c),B=(d.b.c),其中a b c d均为三维列向量,已知行列式
/A/=2,/B/=1\2,则行列式/A+2B/=?
设3*3的矩阵A=(a.b.c),B=(d.b.c),其中a b c d均为三维列向量,已知行列式/A/=2,/B/=1\2,则行列式/A+2B/=?
|A+2B|
= |a+2d,3b,3c|
= |a,3b,3c|+|2d,3b,3c|
= 9|a,b,c|+18|d,b,c|
= 9|A|+18|B|
= 9*2+18*1/2
= 27.