Chapter 1
1) WHAT A MATRIX ACTUALLY IS (INTUITION FIRST)
Forget formulas first.
A matrix is just an organised table of numbers used to represent information.
Example in the slides:
A car company produces two series (U and V) and four models (L, GL, GLX, GLE).
So instead of writing sentences:
Series L GL GLX GLE
U 800 700 600 400
V 200 250 100 150
We write:
A=
[ 800 700 600 400
200 250 100 150]
That is a matrix
Key terminology (VERY IMPORTANT)
Rows → horizontal
Columns → vertical
Matrix dimension = rows × columns
So above matrix = 2 × 4 matrix
Special terms
Row vector → one row
Column vector → one column
Scalar → single number
b63d397f-6131-4cdb-ab95-26c8d46…
Why matrices exist
They allow us to:
• store data
• calculate totals fast
• solve many equations at once
• model economics, statistics and finance problems
You are basically learning a language computers and statistics use.
, 2) ACCESSING INFORMATION (READING A MATRIX)
Think of matrix like Excel.
A [2,4] → row 2 column 4
= series V, model GLE = 150
So a matrix is just a structured dataset.
3) MATRIX OPERATIONS
Now maths rules.
Equality of matrices
Two matrices are equal if:
1. Same size
2. Every number same position equal
Addition & subtraction
You add element-by-element:
[1 4] + [1 2] = [2 6]
[2 5] [2 3] [4 8]
You cannot add matrices of different sizes.
Scalar multiplication
Multiply every number by constant:
4×
[2 7]
[9 3]
=
[8 28]
[36 12]
4) MATRIX MULTIPLICATION (THE BIG ONE)
This is where students struggle.
Rule
You can multiply only if:
columns of A = rows of B
What multiplication means conceptually
Matrix multiplication = combining information
Example in slides:
Production × Profit = Total profit
So matrix multiplication is basically:
weighted totals
1) WHAT A MATRIX ACTUALLY IS (INTUITION FIRST)
Forget formulas first.
A matrix is just an organised table of numbers used to represent information.
Example in the slides:
A car company produces two series (U and V) and four models (L, GL, GLX, GLE).
So instead of writing sentences:
Series L GL GLX GLE
U 800 700 600 400
V 200 250 100 150
We write:
A=
[ 800 700 600 400
200 250 100 150]
That is a matrix
Key terminology (VERY IMPORTANT)
Rows → horizontal
Columns → vertical
Matrix dimension = rows × columns
So above matrix = 2 × 4 matrix
Special terms
Row vector → one row
Column vector → one column
Scalar → single number
b63d397f-6131-4cdb-ab95-26c8d46…
Why matrices exist
They allow us to:
• store data
• calculate totals fast
• solve many equations at once
• model economics, statistics and finance problems
You are basically learning a language computers and statistics use.
, 2) ACCESSING INFORMATION (READING A MATRIX)
Think of matrix like Excel.
A [2,4] → row 2 column 4
= series V, model GLE = 150
So a matrix is just a structured dataset.
3) MATRIX OPERATIONS
Now maths rules.
Equality of matrices
Two matrices are equal if:
1. Same size
2. Every number same position equal
Addition & subtraction
You add element-by-element:
[1 4] + [1 2] = [2 6]
[2 5] [2 3] [4 8]
You cannot add matrices of different sizes.
Scalar multiplication
Multiply every number by constant:
4×
[2 7]
[9 3]
=
[8 28]
[36 12]
4) MATRIX MULTIPLICATION (THE BIG ONE)
This is where students struggle.
Rule
You can multiply only if:
columns of A = rows of B
What multiplication means conceptually
Matrix multiplication = combining information
Example in slides:
Production × Profit = Total profit
So matrix multiplication is basically:
weighted totals
