Matrix Operations
A matrix is a rectangular array of numbers. Matrices are added element-by-element and multiplied using row-by-column dot products. They are used in coding, economics, and computer graphics.
What You Need to Know
Key Concept Diagram
Matrix addition: add corresponding elements (matrices must have same dimensions)
Scalar multiplication: multiply every element by the scalar
Matrix multiplication: (AB)_{ij} = sum of row i of A times column j of B
The identity matrix I has 1s on the diagonal and 0s elsewhere; AI = IA = A
Key Vocabulary
Matrix
A rectangular array of numbers arranged in rows and columns
Element
A single number in a matrix, identified by its row and column position
Identity matrix
A square matrix with 1s on the diagonal and 0s elsewhere
Dimensions
The size of a matrix, given as rows x columns (e.g. 2x3)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Add the matrices [1 2; 3 4] and [5 6; 7 8].
Question 2
Multiply the matrix [2 3; 1 4] by scalar 3.
Question 3
What are the dimensions of the product of a 2x3 matrix and a 3x2 matrix?
Key Concepts Summary
- ●Matrix addition: add corresponding elements (matrices must have same dimensions)
- ●Scalar multiplication: multiply every element by the scalar
- ●Matrix multiplication: (AB)_{ij} = sum of row i of A times column j of B
- ●The identity matrix I has 1s on the diagonal and 0s elsewhere; AI = IA = A