Algebra Question

hello,

the file is attached down below

its four questions

thanks

MAS164: Fundamentals of Mathematics
Semester 1, 2021
Assignment 2 – Due 5pm, Friday 26 March
This assignment is worth 55 marks, with 5 marks reserved for presentation. Please
note that marks will be deducted for solutions that are not properly presented, for
working that is inadequate, or for untidy work.
Always show full working. Where possible give the exact answer.
1. [20 marks] Consider the following matrices

A=
2x
3
1
−2


B=
2
0
7 6
2 −1

7
C= 0
−3


1
5
2

D=
1
−3
4
−2

Where possible, find the following. If not possible give the reason.
(a) AB
[4 marks]
(b) DA
[3 marks]
(c) B + C
[2 marks]
(d) AC
[2 marks]
(e) 2D + BC
[6 marks]
(f) The value of x for which A does not have an inverse.
[3 marks]
2. [11 marks] Consider

1 0
A =  −3 2
5 2
the three matrices



2
3
0
B= 0 
4
−2
−4
1 
C=
−6
12
8

−2
3
1

2
3 
−1
(a) Show by calculating the product AC that C is the inverse matrix of A [6
marks]
(b) Hence calculate the solution to the linear system AX = B.
3. [7 marks] Simplify
(1 − 2x)3 (x3 y)4 z 5
1
3−2 (16×4 ) 2 y 5 (1 − 2x)−2 z −3
1
[5 marks]
4. [12 marks] Solve the following inequality problems. You must give your answer
using interval notation. You must also give you answer in graphical form
(using the number line).
(a) 2x − 5 < −8 or 7 − 2x ≤ x + 4 [6 marks] (b) 3 − 2x < 4 and 6x − 3 ≤ 4x + 1 [6 marks] • Note: There are penalties for late assignments. You must contact your tutor before the due date if you have difficulties making the deadline.