一些线代问题设n阶矩阵A,B,C满足AB=BC=CA=E,则A平方+B平方+C平方= 2.已知a1=(1,1,1),a2=(a,0,b),a3=(1,3,2),若a1,a2,a3线性相关,则a与b满足?3.由向量组a1=( 1 ) ,a2= ( -1 ) ,求一正交向量组 b1=?b2=?
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![一些线代问题设n阶矩阵A,B,C满足AB=BC=CA=E,则A平方+B平方+C平方= 2.已知a1=(1,1,1),a2=(a,0,b),a3=(1,3,2),若a1,a2,a3线性相关,则a与b满足?3.由向量组a1=( 1 ) ,a2= ( -1 ) ,求一正交向量组 b1=?b2=?](/uploads/image/z/8931212-44-2.jpg?t=%E4%B8%80%E4%BA%9B%E7%BA%BF%E4%BB%A3%E9%97%AE%E9%A2%98%E8%AE%BEn%E9%98%B6%E7%9F%A9%E9%98%B5A%2CB%2CC%E6%BB%A1%E8%B6%B3AB%3DBC%3DCA%3DE%2C%E5%88%99A%E5%B9%B3%E6%96%B9%2BB%E5%B9%B3%E6%96%B9%2BC%E5%B9%B3%E6%96%B9%3D+2.%E5%B7%B2%E7%9F%A5a1%3D%281%2C1%2C1%29%2Ca2%3D%28a%2C0%2Cb%29%2Ca3%3D%281%2C3%2C2%29%2C%E8%8B%A5a1%2Ca2%2Ca3%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%2C%E5%88%99a%E4%B8%8Eb%E6%BB%A1%E8%B6%B3%3F3.%E7%94%B1%E5%90%91%E9%87%8F%E7%BB%84a1%3D%28+1++%29++%2Ca2%3D+%28+-1++%29+%2C%E6%B1%82%E4%B8%80%E6%AD%A3%E4%BA%A4%E5%90%91%E9%87%8F%E7%BB%84+b1%3D%3Fb2%3D%3F)
一些线代问题设n阶矩阵A,B,C满足AB=BC=CA=E,则A平方+B平方+C平方= 2.已知a1=(1,1,1),a2=(a,0,b),a3=(1,3,2),若a1,a2,a3线性相关,则a与b满足?3.由向量组a1=( 1 ) ,a2= ( -1 ) ,求一正交向量组 b1=?b2=?
一些线代问题
设n阶矩阵A,B,C满足AB=BC=CA=E,则A平方+B平方+C平方=
2.已知a1=(1,1,1),a2=(a,0,b),a3=(1,3,2),若a1,a2,a3线性相关,则a与b满足?
3.由向量组a1=( 1 ) ,a2= ( -1 ) ,求一正交向量组 b1=?b2=?
1 2
一些线代问题设n阶矩阵A,B,C满足AB=BC=CA=E,则A平方+B平方+C平方= 2.已知a1=(1,1,1),a2=(a,0,b),a3=(1,3,2),若a1,a2,a3线性相关,则a与b满足?3.由向量组a1=( 1 ) ,a2= ( -1 ) ,求一正交向量组 b1=?b2=?
(1)A^2+B^2+C^2=A(BC)A+B(CA)B+C(AB)C
=(AB)(CA)+(BC)(AB)+(CA)(BC)
=E^2+E^2+E^2
=3E .
(2)线性相关,则行列式为 0 ,展开可得 0+3a+b-0-2a-3b=a-2b=0 .
(3)b1=(1,1),b2=(-1,1)