a11 a12 Cll C In C21c22 lmI lm =a1b1;+a12b2+…+anb 11C12 In 21C 22 n i1 i2 n n
m m m n ij n n c c c c c c c c c c 1 2 21 22 2 11 12 1 = rj j j i i i r b b b a a a 2 1 1 2
例1 B=00 10-1 0-1 AB 00 10 BA=00 0
− − = 1 0 0 0 1 1 0 1 0 1 0 1 AB − = 0 0 0 1 − − = 0 1 0 1 0 1 1 0 0 0 1 1 BA − − − = 1 0 1 0 0 0 1 1 1 例1
例2 b3) a3b, a3b2 a3b3 a,6+a262+a3b3
例2 ( ) 1 2 3 3 2 1 b b b a a a = 3 1 3 2 3 3 2 1 2 2 2 3 1 1 1 2 1 3 a b a b a b a b a b a b a b a b a b ( ) 3 2 1 1 2 3 a a a b b b = a1b1 + a2b2 + a3b3
例3 00
例3 0 0 0 1 0 0 1 0 = 0 0 0 1 0 0 1 0 0 0 0 1 = 0 0 0 0
例4 ax, tax+.+.x=b 12 nn a21x,+a222+.+arnn=b, ax1+a,,+…+a.=b n nn n 12 n 令A 2n b 2 mn 则方程组可写作A=b
例4 + + + = + + + = + + + = m m m n n m n n n n a x a x a x b a x a x a x b a x a x a x b 1 1 2 2 2 1 1 2 2 2 2 2 1 1 1 1 2 2 1 1 = = = m m m n n m n n b b b b x x x x a a a a a a a a a A 2 1 2 1 1 2 2 1 2 2 2 1 1 1 2 1 令 , , 则方程组可写作Ax = b