Page 29 - Past Year

27 | P a g e

5  2 3  a 2  36

26. If P    1  4 3 , P      b  2 24 and PQ  4I , where I is the 3x3 identity

 3  1 2    26  2 c  

matrix, determine the values of a, b and c.

 1 2  1 

27. A and B are square matrices such that BA = B . If B  -1   1 0 1    , find A and
-1
 1  
 1 2 
hence, A.

 2 3  1

28. Given the matrix A    0 1  4 .

 
  5 6  1 

(a) Determine the adjoint matrix of A.

-1
(b) By using the result in (a) above, find A . Hence, solve the system of linear equations
below

2x  3y z   5
y  4z  
4
 5x  6y z  9


 2 3 4  9  27 3 




1
29. Given C    5 0 1 and D   7  26 18 . Find CD and hence determine C .



    
 8 9 3   45 6 15 

 7 2
2
I
30. (a) If Y    , show that Y satisfies the equation Y  8Y   O with I is an
 3 1 
identity matrix 2 2 . Hence, find Y 1  .