Original Mathematics Notes: Matrices & Vectors
1. Introduction
Matrices are rectangular arrays of numbers arranged in rows and columns. Vectors are
quantities that have both magnitude and direction.
2. Matrices
Common operations include matrix addition, subtraction, scalar multiplication, matrix
multiplication, and finding determinants of square matrices.
Worked Example 1
Add the matrices:
A = [[1, 2], [3, 4]]
B = [[5, 6], [7, 8]]
Solution:
A + B = [[6, 8], [10, 12]].
3. Determinants
For a 2 × 2 matrix [[a, b], [c, d]], the determinant is ad − bc.
Worked Example 2
Find the determinant of [[2, 3], [4, 5]].
Determinant = (2 × 5) − (3 × 4) = 10 − 12 = −2.
4. Vectors
A vector is written as <x, y> or in column form. The magnitude of vector <a, b> is √(a² + b²).
Worked Example 3
Find the magnitude of vector <3, 4>.
Magnitude = √(3² + 4²) = √25 = 5.
5. Applications
Matrices are used in computer graphics, cryptography, economics, and engineering. Vectors
are used in physics, navigation, robotics, and aviation.
Practice Questions
1. Add [[2, 1], [0, 3]] and [[4, 2], [5, 1]].
2. Find the determinant of [[6, 2], [1, 4]].
3. Find the magnitude of vector <5, 12>.
4. Multiply vector <2, 3> by scalar 4.
1. Introduction
Matrices are rectangular arrays of numbers arranged in rows and columns. Vectors are
quantities that have both magnitude and direction.
2. Matrices
Common operations include matrix addition, subtraction, scalar multiplication, matrix
multiplication, and finding determinants of square matrices.
Worked Example 1
Add the matrices:
A = [[1, 2], [3, 4]]
B = [[5, 6], [7, 8]]
Solution:
A + B = [[6, 8], [10, 12]].
3. Determinants
For a 2 × 2 matrix [[a, b], [c, d]], the determinant is ad − bc.
Worked Example 2
Find the determinant of [[2, 3], [4, 5]].
Determinant = (2 × 5) − (3 × 4) = 10 − 12 = −2.
4. Vectors
A vector is written as <x, y> or in column form. The magnitude of vector <a, b> is √(a² + b²).
Worked Example 3
Find the magnitude of vector <3, 4>.
Magnitude = √(3² + 4²) = √25 = 5.
5. Applications
Matrices are used in computer graphics, cryptography, economics, and engineering. Vectors
are used in physics, navigation, robotics, and aviation.
Practice Questions
1. Add [[2, 1], [0, 3]] and [[4, 2], [5, 1]].
2. Find the determinant of [[6, 2], [1, 4]].
3. Find the magnitude of vector <5, 12>.
4. Multiply vector <2, 3> by scalar 4.
