Assignment 2

Show your working for the following questions using Microsoft Word’s Equations:

If A = -5  1     and   B =    3    -6

3       2                     2    -3

Find:-            a) A²      b) determinant A             c) A^T  d) B^-1            (5 marks)

 

a) Using matrix method solve the following simultaneous equations

5x + y = 9

2x – 2y = 6                                                     (8 marks)

 

Find the determinant of the following matrix

4       -2       3                        (4 marks)

 0        3        2        5       -2       7

 

If told that |A| = 48 what are the possible value(s) for x

3x        4x

A =            3          2x                          ( 4 marks)

 

 Given that f(x) = 2x + 5 g(x) = 2x – 6     and h(x) = x² – 5                                                    x

Find:-                      i) f(-4) =                      ii) h[f(-6)] =                            iii) f[g(-2)]  = iv) h_ᴏf(x)            v) g^-1(x) =                    (2, 3, 3,4, 4 marks)

 

Given the functions             g(x) =   5x + 1      find g^-1(x)

                                      2x – 6                                    (5 marks)

 

 Two numbers when multiplied equals 63.

one number is x and the other number is 2 less than x

Represent the information given in equation form

Express as a quadratic equation

Solve the quadratic equation to find possible values for x

The two number are positive numbers, what are their possible values.

(10 marks)

Solve the following quadratic equations ( hint use the quadratic formula)

6. a) 2x² – x – 6 = 0              b) 6x² + 7x – 5 = 0                   (5 Marks)

 

Find the equation of the line joining the points (4, 9) and (-1, 0)

(5 marks)

Find the equation of the line passing through the point (-2, 7) and perpendicular to the line 3y = 8 – 4x                                      (5 marks)