Division of Natural Sciences
Department of Mathematics, Physics and Statistics
MTH 2105 – Linear Algebra 1
Tutorial Worksheet 3
Instruction: Everyone is required to complete all the questions. However, only those who signed
up to present in Week 4 will need to present their solutions, each presenter will be randomly
assigned a question.
•
Questions
1. Use cofactor expansion to find the determinant of the 4 × 4 matrix given below:
3 2 0
4 1 3
𝑋=(
2 −1 3
5 0 2
5
−1
)
6
−1
2. Use Gaussian Elimination to find the solution to the system of equations given below:
5𝑥 − 5𝑦 − 15𝑧 = 40
{ 4𝑥 − 2𝑦 − 6𝑧 = 19
3𝑥 − 6𝑦 − 17𝑧 = 41
3. Use Gauss-Jordan Method to find the solution to the system of equations below (you may need
to use free variables)
4𝑥1 − 8𝑥2 − 2𝑥3 = 0
{3𝑥1 − 5𝑥2 − 2𝑥3 = 0
2𝑥1 − 8𝑥2 + 𝑥3 = 0
4. Use row reduction to show that
1
|𝑎
𝑎2
1
𝑏
𝑏2
1
𝑐 | = (𝑏 − 𝑎)(𝑐 − 𝑎)(𝑐 − 𝑏)
𝑐2
END