A column matrix has dimensions $n \times 1$, where $n$ is the number of rows.
Column matrices are useful for representing solutions in systems of linear equations.
They can be added to or subtracted from other column matrices of the same dimension.
The transpose of a column matrix becomes a row matrix.
Scalar multiplication with a column matrix involves multiplying each entry by the scalar.
Review Questions
What are the dimensions of a column matrix with 4 elements?
How do you perform scalar multiplication on a column matrix?
What does the transpose of a column matrix look like?
Related terms
Row Matrix: A row matrix consists of a single row and multiple columns, often used to represent coefficients in linear equations.
Matrix Transpose: The transpose of a matrix is obtained by swapping its rows with its columns.
Vector: In linear algebra, a vector can be represented as either a row or column matrix and is used to denote quantities having both magnitude and direction.