Linear algebra Introduction
Matrices
Apply several weighted sums at once.
Before this
The intuition
A matrix is a rectangular table of numbers. Multiplying a matrix by a vector computes one dot product per row, producing a new vector.
A concrete example
Rows [1, 0] and [0, 2] applied to [3, 4] produce [3, 8]. The first coordinate stays the same; the second doubles.
What to remember
For matrix–vector multiplication, each row must have as many entries as the input vector.
Check your understanding
What does a matrix with rows [1, 0] and [0, 1] do?
Reveal explanation
It leaves the vector unchanged: this is the identity matrix.