Using matrix method solve the following simultaneous equations.Find the determinant of the following matrix

IYMS1001 – Improving Your Math Skills 

Tutorial Assignment 2 (40%)

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

 

1. 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)

2. a) Using matrix method solve the following simultaneous equations

5x + y = 9

                        2x – 2y = 6                                   (8 marks)

b) Find the determinant of the following matrix

4       -2       3

0        3        2

5       -2       7                                (4 marks)       

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

  3x         4x

A =            3          2x          ( 4 marks)

3. 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)

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

                                   2x – 6               (5 marks)

5. Two numbers when multiplied equals 63.

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

a) Represent the information given in equation form

b) Express as a quadratic equation

c) Solve the quadratic equation to find possible values for x

d) The two number are positive numbers, what are their possible values.   (10 marks)

 

6. Solve the following quadratic equations ( hint use the quadratic formula)                                                                     a) 2x² – x – 6 = 0              b) 6x² + 7x – 5 = 0         (5 Marks)
7. Find the equation of the line joining the points (4, 9) and (-1, 0) (5 marks)

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