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__Question 1:__** [6 Marks]**

Let ** **

**, **

**, **and** **

**.** Express the indicated logarithm in terms of

** **and** **

**:**

**i)**

**[2 Marks]**

**ii)**

**[2 Marks]**

**iii)**

**[2 Marks]**

__Question 2:__** [8 Marks]**

**a)**If

is invested at a nominal rate of

compounded continuously, find the compound amount after

years.**[3 Marks]**

**b)**How many years will it take for a principal of

to double at the interest rate of

compounded monthly? **[5 Marks]**

__Question 3:__** [10 Marks]**

**a)**Construct the matrix

if

is a

and

**[4 Marks]**

**b)**Solve the matrix equation:

**[6 Marks]**

__Question 4:__** [12 Marks]**

Given the matrices:

Find:

**a)**

**[3 Marks]**

**b)**

**[4 Marks]**

**c)**

** [5 Marks]**

__Question 5:__** [9 Marks]**

**a)**Solve the following system by using the inverse:

**[5 Marks]**

**b)**Solve the following system by the method of reduction:

**[4 Marks]**