UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology
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MAT3700: Linear Algebra
Assignment 03 — Semester 1, 2026
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MAT3700
Module Code:
Linear Algebra
Module Name:
Assignment 03
Assignment:
2026
Due Date:
30
Total Marks:
Submitted in partial fulfilment of the requirements for MAT3700 — UNISA 2026
, UNISA | MAT3700 Assignment 03 — 2026
Question 1: Eigenvalues of Matrix B (5 marks)
2 4
Question: If B = , find the eigenvalues of B.
1 5
Step 1: Characteristic equation
det(B − λI) = 0
Step 2: Subtract λ from the diagonal
2−λ 4
B − λI =
1 5−λ
Step 3: Compute the determinant
(2 − λ)(5 − λ) − (4)(1) = 0
Step 4: Expand
(2 − λ)(5 − λ) = 10 − 2λ − 5λ + λ2 = λ2 − 7λ + 10
Therefore:
λ2 − 7λ + 10 − 4 = 0 =⇒ λ2 − 7λ + 6 = 0
Step 5: Factorise
Two numbers that multiply to 6 and add to −7 are −6 and −1:
(λ − 6)(λ − 1) = 0
Step 6: Eigenvalues
λ=6 and λ=1
Page 2 of 11
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MAT3700: Linear Algebra
Assignment 03 — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MAT3700
Module Code:
Linear Algebra
Module Name:
Assignment 03
Assignment:
2026
Due Date:
30
Total Marks:
Submitted in partial fulfilment of the requirements for MAT3700 — UNISA 2026
, UNISA | MAT3700 Assignment 03 — 2026
Question 1: Eigenvalues of Matrix B (5 marks)
2 4
Question: If B = , find the eigenvalues of B.
1 5
Step 1: Characteristic equation
det(B − λI) = 0
Step 2: Subtract λ from the diagonal
2−λ 4
B − λI =
1 5−λ
Step 3: Compute the determinant
(2 − λ)(5 − λ) − (4)(1) = 0
Step 4: Expand
(2 − λ)(5 − λ) = 10 − 2λ − 5λ + λ2 = λ2 − 7λ + 10
Therefore:
λ2 − 7λ + 10 − 4 = 0 =⇒ λ2 − 7λ + 6 = 0
Step 5: Factorise
Two numbers that multiply to 6 and add to −7 are −6 and −1:
(λ − 6)(λ − 1) = 0
Step 6: Eigenvalues
λ=6 and λ=1
Page 2 of 11
