3×1

3×1, read as “three by one,” can refer to two related ideas in mathematics. It denotes either the product of the numbers 3 and 1, or the dimension of a matrix or array with three rows and one column.

In arithmetic, 3×1 equals 3. Multiplication is often interpreted as repeated addition: three copies of the value 1 sum to 3 (1 + 1 + 1 = 3). More generally, any number multiplied by 1 leaves the number unchanged, so a×1 = a; therefore 3×1 = 3. The operation is commutative with respect to the factors of positive integers, so 3×1 = 1×3 = 3.

In linear algebra, a 3×1 matrix is a column vector with three components, that is, a three-entry arrangement in a single column. It is typically written as [a; b; c] or [a, b, c]^T and represents a vector in three-dimensional space. The transpose of a 3×1 matrix is a 1×3 row vector. The 3×1 form is common for storing coordinates and for multiplying by suitable matrices (for example, a 3×1 vector multiplied by a 1×n matrix yields a 3×n matrix).

In applications, 3×1 column vectors appear in geometry, computer graphics, physics, and systems of linear equations as representations of points, directions, or state vectors.