AMP STUDY NOTES
MAT1503 · LINEAR ALGEBRA
Complete Module
Additional Practice Problems
All four chapters’ practice problems combined into a single volume,
in order, for the full module.
Chapter 1 — Systems of Linear Equations and Matrices
Chapter 2 — Determinants
Chapter 3 — Vectors in 2-Space and 3-Space
Chapter 4 — Complex Numbers
PRACTICE PROBLEMS · ALL CHAPTERS
Independent study material. Independently authored revision aid, not affiliated with, endorsed by, or sourced
from UNISA or any official assessment body. © AMP Study Notes.
,AMP STUDY NOTES
MAT1503 · LINEAR ALGEBRA
Chapter 1
Additional Practice Problems
Six practice problems in the style commonly seen in MAT1503
assessments, spanning system-solving, invertibility, matrix
arithmetic, and symmetric matrices — each with a complete,
independently worked solution.
PRACTICE PROBLEMS · CHAPTER 1
Independent study material. These are original practice problems, written to match the style and difficulty of
typical MAT1503 assessments. They are not reproductions of any specific past exam, assignment, or memo, are
not affiliated with, endorsed by, or sourced from UNISA or any official assessment body, and include
independently worked, verified solutions. © AMP Study Notes.
, AMP Study Notes — MAT1503 — Chapter 1 Practice Problems
Chapter 1: Additional Practice Problems
Six problems covering the full spread of Chapter 1's exam-relevant skills, each with a complete solution. Attempt
each problem before reading its solution.
Problem 1 — Solving a System by Gaussian Elimination
Solve the following system completely by reducing its augmented matrix to row-echelon form:
Solution. Interchange and so the leading entry is already 1:
Eliminate below the first pivot with and :
The last row gives , so . Back-substitute into row 2: . Back-
substitute into row 1: .
Answer: (unique solution).
Page 2 of 5
MAT1503 · LINEAR ALGEBRA
Complete Module
Additional Practice Problems
All four chapters’ practice problems combined into a single volume,
in order, for the full module.
Chapter 1 — Systems of Linear Equations and Matrices
Chapter 2 — Determinants
Chapter 3 — Vectors in 2-Space and 3-Space
Chapter 4 — Complex Numbers
PRACTICE PROBLEMS · ALL CHAPTERS
Independent study material. Independently authored revision aid, not affiliated with, endorsed by, or sourced
from UNISA or any official assessment body. © AMP Study Notes.
,AMP STUDY NOTES
MAT1503 · LINEAR ALGEBRA
Chapter 1
Additional Practice Problems
Six practice problems in the style commonly seen in MAT1503
assessments, spanning system-solving, invertibility, matrix
arithmetic, and symmetric matrices — each with a complete,
independently worked solution.
PRACTICE PROBLEMS · CHAPTER 1
Independent study material. These are original practice problems, written to match the style and difficulty of
typical MAT1503 assessments. They are not reproductions of any specific past exam, assignment, or memo, are
not affiliated with, endorsed by, or sourced from UNISA or any official assessment body, and include
independently worked, verified solutions. © AMP Study Notes.
, AMP Study Notes — MAT1503 — Chapter 1 Practice Problems
Chapter 1: Additional Practice Problems
Six problems covering the full spread of Chapter 1's exam-relevant skills, each with a complete solution. Attempt
each problem before reading its solution.
Problem 1 — Solving a System by Gaussian Elimination
Solve the following system completely by reducing its augmented matrix to row-echelon form:
Solution. Interchange and so the leading entry is already 1:
Eliminate below the first pivot with and :
The last row gives , so . Back-substitute into row 2: . Back-
substitute into row 1: .
Answer: (unique solution).
Page 2 of 5
