Question

用矩阵的初等变换求方阵的逆阵：[3 2 1] [3 1 5] [3 2 3]

Answer 1

(A,E) =|>

|3 2 1 1 0 0|

|3 1 5 0 1 0|

|3 2 3 0 0 1|

=|>

|1 2/3 1/3 1/3 0 0|

|1 1/3 5/3 0 1/3 0|

|1 2/3 1 0 0 1/3|

=|>

|1 2/3 1/3 1/3 0 0|

|0 -1/3 4/3 -1/3 1/3 0|

|0 0 2/3 -1/3 0 1/3|

=|>

|1 2/3 1/3 1/3 0 0|

|0 1 -4 1 -1 0|

|0 0 1 -1/2 0 1/2|

=|>

|1 0 0 7/6 2/3 -3/2|

|0 1 0 -1 -1 2|

|0 0 1 -1/2 0 1/2|

所以逆矩阵为

|7/6 2/3 -3/2|

|-1 -1 2|

|-1/2 0 1/2|