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25 | P a g e

1  3 
 p 2  1    4 5 
(b) Find the values of p and q, if    2  1     .
  3 0 q    11  19 
 4  5  

2
3
21. (a) Given matrix B  B  6B  where B is a 3 3 matrix and I is a 3 3 identity
I
matrix.

-1
2
1
B
(i) By using B onto the equation, show that B  B   6 .
I

1  2 1

-1
(ii) Hence , if B    1  1 0 , determine B .

3  1
 1 
(b) A system linear equations is given as follows.
3x  6y  3z  1
3x  3y   2
9x  3y  3z  1

(i) Write the above system of linear equations in the form of 3BX  C where B

is the matrix from (a) (ii) above, X is an unknown column matrix and C is a

constant column matrix.

(ii) Hence, by using the inverse matrix, solve the above system of linear

equations.

2  0   2  4

22. (a) Given B    0 4 , and C    1  3   , find Y such that YC=B.

 5   1 

 0 2 T 6 1 

T
(b) Find the transpose matrix, A if3A  2  5 2      2  .
T

  1 3   2 2 6 