Question

急线性代数设A=[a1,a2,b1],B=[a1,a2,b2],其中a1a2b1b2均为三维列向量且|A|=2,|A-3

Answer 1

|A-3B|

= |a1-3a1,a2-3a2,b1-3b2|

= |-2a1,-2a2,b1-3b2|

= (-2)*(-2)|a1,a2,b1-3b2|

= 4 |a1,a2,b1-3b2|

= 4 (|a1,a2,b1|-3|a1,a2,b2|)

= 4|A| - 12|B|

所以 -4 = 4*2 - 12|B|

得 |B| = 1.