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18 | P a g e

CHAPTER 4: MATRICES AND SYSTEMS OF LINEAR EQUATIONS

 3 6 3   1  1 4 
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

T
1. Given the matrices P    3  3 0 and Q   1  2 5 . Find PQ . Hence, find P  1



    
 9 3 3   1 1 3 
.
 4  1 6  33 2  17
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
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2. Given the matrix A    y 9 3 and its cofactor matrix is 10 4  6 .



    57  
 x 1 4   6 37 
2
Show that x  .
Hence, find
(a) the value of y.
(b) the determinant, |A|.
(c) the adjoint matrix, Adj (A).


1
(d) the inverse matrix, A .

 3 1  1

3. Given A    2 0 4 .

  1 6 5  

T
2A
(a) Find    . A
(b) Determine the minor m21 and cofactor c22 for matrix A.

 1 2 0  2 2  2
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
4. Given A    3 2 1 and B    1  1 1 .


   
 2 4 1    8 0 4 
(a) Show that AB  4I .
(b) Hence,


(i) determine A .
1
(ii) solve the following system of linear equations: