同济大学线性代数第六版答案(20)

⎪⎪⎭

⎫ ⎝⎛⎪⎪⎭⎫ ⎝⎛321332313232212131211321)(x x x a a a a a a a a a x x x (a 11x 1a 12x 2a 13x 3

a 12x 1a 22x 2a 23x 3 a 13x 1a 23x 2

a 33x 3)⎪⎪⎭⎫ ⎝⎛321x x x 322331132112233322222111222x x a x x a x x a x a x a x a +++++=

5 设⎪⎭⎫ ⎝

⎛=3121A ⎪⎭⎫ ⎝⎛=2101B 问 (1)AB BA 吗 解 AB BA

因为⎪⎭⎫ ⎝

⎛=6443AB ⎪⎭⎫ ⎝⎛=8321BA 所以AB BA (2)(A B )2A 22AB B 2吗

解 (A B )2A 22AB B 2 因为⎪⎭⎫ ⎝

⎛=+5222B A ⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛=+52225222)(2B A ⎪⎭⎫ ⎝⎛=2914148

但 ⎪⎭⎫ ⎝

⎛+⎪⎭⎫ ⎝⎛+⎪⎭⎫ ⎝⎛=++43011288611483222B AB A ⎪⎭⎫ ⎝⎛=27151610 所以(A B )2A 22AB B 2

(3)(A B )(A B )A 2B 2吗

解 (A B )(A B )A 2B 2