MAT3700 Assignment 03 Year Module 2026

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




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