Mat,Semester 01, Assignment 01 Solution

NB: DETAILED SOLUTIONS START FROM PAGE 10
ADDENDUM A: Assignments
The multiple-choice assignments will be marked by computer. Hence the closing date is fixed and
no extension of time can be granted.

Before you attempt enter your answers, please study in detail the relevant chapter of the publication
My Studies @ Unisa.

Note that your assignment will not be returned to you. Please keep a record of your answers so
that you can compare them with the worked out solutions.

In each of the following questions, four, five or six possible answers are given. In each case,
mark/select the number of the answer that you think is correct.

For each correct answer you obtain 2 marks and for each incorrect one you may lose 1 mark. The
multiple-choice Assignment 01 counts out of 40 marks.


COMPULSORY ASSIGNMENT FOR THE EXAM
ASSIGNMENT 01
Due date: Monday, 26 April 2021
Total Marks: 40
UNIQUE ASSIGNMENT NUMBER: 637477

ONLY FOR YEAR MODULE

This assignment covers chapter 1 of the prescribed book as well as the study
guide, its specifically based on Study Units 1.1 & 1.2

IMPORTANT
• This is a multiple choice assignment. ALL the questions must be answered. The best way to submit
the assignment is online, using myUnisa. Before answering this assignment, consult the publication
Study @ Unisa on how to use and complete a mark reading sheet.
• Keep your rough work so that you can compare your solutions with those uploaded on myUnisa.
• 2 marks will be awarded for every correct answer.

Question 1: 2 Marks

Which of the following is a linear equation in x; y and z?
1. x − e2 y = 3z, where e = 2.71828 ....
1
2. 2π ln(e z ) − 2y + z = ln(3) − x.
p
3. y −2 + 4y − 2z = 7x.
4. y + 4y − 2z = 7x 3 .



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, MAT1503/001/0/2021


Question 2: 2 Marks

Which of the following is a linear equation in x; y and z?

1. x 2 − e2 y = 3z, where e = 2.71828 ....

2. 2π ln(ez ) − 2y + z = ln(3) − x.
p
3. y −1 + 4y − 2z = 7x.

4. y + 4y − 2z = 7x 3 .


Question 3: 2 Marks

Which of the following is a nonlinear equation in x; y and z?

1. y + 4y − 2z = 7x.

2. 2π ln e−z − 2y + z = ln(3) − x.

3. 7x − 4y − 2z = 0.

4. x − exy = 3z, where e = 2.71828 ....




In the following three questions, draw a table of logical operation in order to boil down statements into
digestible operations through the corresponding logical formulas.

Question 4: 2 Marks

Any homogeneous linear system has one solution or no solution.

1. T ∧ F, where T stands for True and F stands for False.

2. (F ∨ F) ∧ ¬T, where ¬ is the symbol for logical negation.

3. F ∧ (¬ F ∨ T).

4. (T ∨ F) ∧ F.

5. (T ∨ F) ∨ F.




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, Question 5: 2 Marks

Any homogeneous linear system has no solution or infinitely many solutions.

1. T ∧ F, where T stands for True and F stands for False.

2. (F ∨ F) ∧ ¬T, where ¬ is the symbol for logical negation.

3. F ∧ (¬ F ∨ T).

4. (¬T ∨ F) ∨¬ F.

5. (T ∧¬ T) ∧ (¬ F).


Question 6: 2 Marks

Any homogeneous linear system has one solution or infinitely many solutions.

1. T ∧ F, where T stands for True and F stands for False.

2. (¬T ∧¬ F) ∨ (¬ F).

3. F ∧ (¬ F ∨ T).

4. (T ∨ F) ∧ F.

5. (F ∨ F) ∧ ¬T, where ¬ is the symbol for logical negation.


Question 7: 2 Marks

Determine which of the following is the solution set of the linear equation below.

3x − y + z = 2.

1. {(x, y, z) : x = 13 (t − s + 2), y = t, z = s with s, t ∈ R}

2. {(x, y, z) : x = 13 (t + s + 2), y = t, z = s with s, t ∈ R}

3. {(x, y, z) : x = 13 (t − s − 2), y = t, z = s with s, t ∈ R}

4. {(x, y, z) : x = − 13 (2 + t − s), y = t, z = s with s, t ∈ R}




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