math 1 assignment

I’m working on a Mathematics question and need guidance to help me study.

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]