《线性代数》课程教学课件（PPT讲稿，B）第三章 矩阵的运算_3-1 矩阵的运算

1 012 L 1s b bi2 L a21 4 L bat ba L 设A= L ,B= bn L L L am 0m2 L ams mxs b2 L bns -1； L bin 421 022 L 42s 421 b L AB= L L L L b,L 41b1+412bG1+L+41,b1

11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 , , s n s n m m ms s s sn m s s n a a a b b b a a a b b b A B a a a b b b               = =             设 L L L L L L L L L L 11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 = s n s n m m ms s s sn a a a b b b a a a b b b AB a a a b b b             =             L L L L L L L L L L 11 11 12 21 1 1 11 12 12 22 1 2 11 1 12 2 1 21 11 22 21 2 1 21 12 22 22 2 2 21 1 22 2 2 1 11 2 21 1 1 12 2 22 2 1 1 2 s s s s n n s sn s s s s n n s sn m m ms s m m ms s m n m a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b + + + + + + + + + + + + + + + + + + + + + + + + + L L L L L L L L L L L L L 2n ms sn a b            + +  L 11 11 12 21 1 1 s s a b a b a b + + + c11 L

41m 12 L s b br2 L 设A= 22 L A2s L ,B= b22 bin L L L L Am am2 L s mxs B32 L bsn sxn -2-s b 2 L bin L21 02 L AB= 02s b21 2 L bin L L L L 、0ml am2 L Bst 民2 L bsn 41b1+a1b21+L+a1sb,141b2+4zbg+L+41,b2

11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 , , s n s n m m ms s s sn m s s n a a a b b b a a a b b b A B a a a b b b               = =             设 L L L L L L L L L L 11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 = s n s n m m ms s s sn a a a b b b a a a b b b AB a a a b b b             =             L L L L L L L L L L 11 11 12 21 1 1 11 12 12 22 1 2 11 1 12 2 1 21 11 22 21 2 1 21 12 22 22 2 2 21 1 22 2 2 1 11 2 21 1 1 12 2 22 2 1 1 2 s s s s n n s sn s s s s n n s sn m m ms s m m ms s m n m a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b + + + + + + + + + + + + + + + + + + + + + + + + + L L L L L L L L L L L L L 2n ms sn a b            + +  L 11 12 12 22 1 2 s s a b a b a b 11 11 12 21 1 1 + + + L s s a b a b a b + + + L 12 c

011 %12 L s b br L 02 L 设A= ,B= b21 b22 L bg L L L L Am Am2 L Bst b32 L 412 L 01s b2 L L L AB= dz az 42s ba b22 L L L L 0m2 L ms B,2 L 41b1+4zb21+L+41b14b2+azb2+L+a1,b2

11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 , , s n s n m m ms s s sn m s s n a a a b b b a a a b b b A B a a a b b b               = =             设 L L L L L L L L L L 11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 = s n s n m m ms s s sn a a a b b b a a a b b b AB a a a b b b             =             L L L L L L L L L L 11 11 12 21 1 1 11 12 12 22 1 2 11 1 12 2 1 21 11 22 21 2 1 21 12 22 22 2 2 21 1 22 2 2 1 11 2 21 1 1 12 2 22 2 1 1 2 s s s s n n s sn s s s s n n s sn m m ms s m m ms s m n m a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b + + + + + + + + + + + + + + + + + + + + + + + + + L L L L L L L L L L L L L 2n ms sn a b            + +  L 11 12 12 22 1 2 s s a b a b a b 11 11 12 21 1 1 + + + L s s a b a b a b + + + L

41 12 L s b br2 L 设A= 22 L A2s L L ,B= bat b22 in L L L 9 Aml am2 L ams mxs ba B32 L 七-5 bu b12 L AB= L21 2 L a2s b21 b22 L L L L L 、Lml am2 L Bst b32 L aubu+aba+aisbst aubz+ab2+L+ab2aubun+arbsitL+absm

11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 , , s n s n m m ms s s sn m s s n a a a b b b a a a b b b A B a a a b b b               = =             设 L L L L L L L L L L 11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 = s n s n m m ms s s sn a a a b b b a a a b b b AB a a a b b b             =             L L L L L L L L L L 11 11 12 21 1 1 11 12 12 22 1 2 11 1 12 2 1 21 11 22 21 2 1 21 12 22 22 2 2 21 1 22 2 2 1 11 2 21 1 1 12 2 22 2 1 1 2 s s s s n n s sn s s s s n n s sn m m ms s m m ms s m n m a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b + + + + + + + + + + + + + + + + + + + + + + + + + L L L L L L L L L L L L L 2n ms sn a b            + +  L 11 12 12 22 1 2 s s a b a b a b 11 11 12 21 1 1 + + + L s s a b a b a b + + + L 1n a b a b a b 11 1 12 2 1 n n s sn + + + c L

1 %12 L b12 L 21 02 L 2s L 设A= L ,B= bat b22 bie L L L am 4m2 L mxs Bst b32 L bsns 412 L 41 b2 L bin L AB= 吃12七-02 b2 L L L aml am2 L ba L anb+arba++asbs aubr2+abz2+L+asb2aubn+arbin+Lasbin a21b1+a22b1+L+42,b1

11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 , , s n s n m m ms s s sn m s s n a a a b b b a a a b b b A B a a a b b b               = =             设 L L L L L L L L L L 11 12 1 11 12 1 21 22 2 21 22 2 1 2 1 2 = s n s n m m ms s s sn a a a b b b a a a b b b AB a a a b b b             =             L L L L L L L L L L 11 11 12 21 1 1 11 12 12 22 1 2 11 1 12 2 1 21 11 22 21 2 1 21 12 22 22 2 2 21 1 22 2 2 1 11 2 21 1 1 12 2 22 2 1 1 2 s s s s n n s sn s s s s n n s sn m m ms s m m ms s m n m a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b a b + + + + + + + + + + + + + + + + + + + + + + + + + L L L L L L L L L L L L L 2n ms sn a b            + +  L 11 12 12 22 1 2 s s a b a b a b 11 11 12 21 1 1 + + + L s s a b a b a b + + + L 21 c 11 1 12 2 1 n n s sn a b a b a b + + + L 21 11 22 21 2 1 s s a b a b a b + + + L