Exercise 4.3.26

Answers

1.
We have that
c11 = (−1)2 det ⁡ ((~A) 11) = A22,
c12 = (−1)3 det ⁡ ((~A) 12) = −A21,
c21 = (−1)3 det ⁡ ((~A) 21) = −A12,
c22 = (−1)4 det ⁡ ((~A) 22) = A11.

So the adjoint of matrix A is

( A22 −A12 −A21 A11 ) .
2.
The adjoint of that matrix is (16 0 0 0 16 0 0 0 16 ).

3.
The adjoint of that matrix is (10 0 0 0 −20 0 0 0 −8 ).

4.
The adjoint of that matrix is (20−30 20 0 15 −24 0 0 12 ).

5.
The adjoint of that matrix is ( −3i 0 0 4 −1 + i 0 10 + 16i−5 − 3i3 + 3i ).

6.
The adjoint of that matrix is ( 6 22 12 12 −2 24 21−38−27 ).

7.
The adjoint of that matrix is ( 18 28 −6 −20 −21 37 48 14 −16 ).

8.
The adjoint of that matrix is ( −i −8 + i−1 + 2i 1 − 5i9 − 6i −3i −1 + i −3 3 − i ).

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2011-06-27 00:00
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