Page 513 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

500 Determinants and Matrices Appen. C

Let cofactor m atrix of A be
^11 C ,2 ^13
C.. = ^21 ^22 ^23
^31 C 3 2 ^33

^ 2 1 C 3 .
a d j A = [ Q ] ' [C.] = C , 2 ^ 2 2 ^ 3 2
C , 3 C 2 3 ^ 3 3

Inverse matrix. The inverse A ^ o f a. m atrix A satisfies the relationship
A-^A =AA-^ =I

Orthogonal matrix. A n orthogonal m atrix A satisfies the relationship
A^A = AA^ = /
From the definition of an inverse matrix, it is evident that for an orthogonal matrix
A^' = A~K

C.3 RULES OF MATRIX OPERATIONS
Addition. Tw o m atrices having the same num ber of rows and colum ns can
be added by summing the corresponding elements.
Example C.3-1

1 3 2 1 '2 0 4 ■3 3 6
4 1 1 1 - 2 -3 .5 - 1 -2 _
Multiplication. The product of two m atrices A and B is another m atrix C.

A B = C
The element C^J of C is determ ined by m ultiplying the elements of the /th row in
A by the elements of the j i h colum n in B according to the rule

C,7 = kj
Example C.3-2
1 1 L '2 O'
Let A = 1 2 2 B -- 0 1
1 2 3 3 -1
.
1 1 r ‘2 O' 5 0 '
AB = 1 2 2 0 1 = 8 0 = C
1 2 3 3 -1 11 -1