Question

求四阶矩阵的逆矩阵

Answer 1

(A,E) =

1 3 -5 7 1 0 0 0

0 1 2 3 0 1 0 0

0 0 1 2 0 0 1 0

0 0 0 1 0 0 0 1

r1-7r4,r2-3r4,r3-2r4

1 3 -5 0 1 0 0 -7

0 1 2 0 0 1 0 -3

0 0 1 0 0 0 1 -2

0 0 0 1 0 0 0 1

r1+5r3,r2-2r3

1 3 0 0 1 0 5 -17

0 1 0 0 0 1 -2 1

0 0 1 0 0 0 1 -2

0 0 0 1 0 0 0 1

r1-3r2

1 0 0 0 1 -3 11 -20

0 1 0 0 0 1 -2 1

0 0 1 0 0 0 1 -2

0 0 0 1 0 0 0 1

左边子块化成了单位矩阵,故A可逆,且 A^-1 =

1 -3 11 -20

0 1 -2 1

0 0 1 -2

0 0 0 1