A和B均为3阶矩阵,|A|=1/2,|B|=3,则|3A-1一2A*|=____(A-1为矩阵A的逆矩阵,A*为矩阵A的伴随矩阵) ...
A和B均为3阶矩阵,|A|=1/2,|B|=3,则|3A-1一2A*|=____(A-1为矩阵A的逆矩阵,A*为矩阵A的伴随矩阵)
人气:344 ℃ 时间:2020-06-04 13:15:11
解答
因为(A-1)=(1/|A|) *( A*)=2(A*); |3(A-1) - 2(A*)|=|4A*|;
而且 A为3阶矩阵 ,所以|4A*|=(4的3次方)|A*| = 64|A*|;
而|A*|=|A|的(n-1)次方= |A|的2次方 = 1/4; 故|3(A-1) - 2(A*)|=|4A*|= 64|A*|= 16;
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