MAT2611 Assignment 1 Due 30 April 2026 |Linear Algebra 2|

UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology


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MAT2611: Linear Algebra

Assignment 01 — Semester 1, 2026

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MAT2611
Module Code:
Linear Algebra
Module Name:
Assignment 01
Assignment:
30 April 2026
Due Date:
60
Total Marks:




Submitted in partial fulfilment of the requirements for MAT2611 — UNISA 2026

,UNISA | MAT2611 Assignment 01 — 2026



Problem 1: Element-of vs Subset Relations

Question:

(a) Give an example of a set A such that there is a set B with B ∈ A but B ̸⊆ A.

(b) Give an example of a set A such that there is a set B with B ⊆ A but B ∈
/ A.


1(a) Solution


Let A = {{1, 2}, 3} and B = {1, 2}.

Checking B ∈ A:

B = {1, 2} is an element of A because {1, 2} appears directly inside A as a member. Therefore
B ∈ A. ✓

Checking B ̸⊆ A:

For B ⊆ A, every element of B must also be an element of A. The elements of B are 1 and 2.


• Is 1 ∈ A? The elements of A are {1, 2} and 3. The number 1 is not directly an element of
A.
• Therefore B ̸⊆ A. ✓

Key Distinction
B ∈ A asks: “Is B listed as a member of A?”
B ⊆ A asks: “Is every element inside B also inside A?”
These are different questions, and a set can satisfy one without satisfying the other.



1(b) Solution


Let A = {1, 2, 3} and B = {1, 2}.

Checking B ⊆ A:

Every element of B must be an element of A.

• 1 ∈ A? Yes.
• 2 ∈ A? Yes.



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, UNISA | MAT2611 Assignment 01 — 2026


Therefore B ⊆ A. ✓

Checking B ∈
/ A:

The elements of A are 1, 2, and 3. The set {1, 2} does not appear as a listed member of A.
Therefore B ∈
/ A. ✓




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