Introduction to Matrices
A matrix is a rectangular array of numbers used to represent and solve systems of linear equations and transformations.
What You Need to Know
Key Concept Diagram
A matrix is described by its order (rows × columns); a 2×3 matrix has 2 rows and 3 columns
Matrices can be added or subtracted only when they have the same order
Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second
The identity matrix I acts like the number 1 in multiplication: AI = IA = A
Key Vocabulary
Matrix
A rectangular array of numbers arranged in rows and columns, enclosed in brackets
Order
The dimensions of a matrix expressed as rows × columns (e.g. 2×3)
Transpose
A new matrix formed by swapping the rows and columns of the original
Determinant
A scalar value calculated from a square matrix that indicates whether the matrix has an inverse
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the order of a matrix with 3 rows and 4 columns?
Question 2
Two matrices A and B can be added if:
Question 3
If A is a 2×3 matrix and B is a 3×2 matrix, what is the order of AB?
Key Concepts Summary
- ●A matrix is described by its order (rows × columns); a 2×3 matrix has 2 rows and 3 columns
- ●Matrices can be added or subtracted only when they have the same order
- ●Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second
- ●The identity matrix I acts like the number 1 in multiplication: AI = IA = A