Types of matrices for JEE

Formula

Row matrix: order \(1\times n\); column matrix: order \(m\times 1\); square matrix: order \(n\times n\); rectangular matrix: \(m\times n,\ m\ne n\); zero matrix: all entries \(0\); diagonal matrix: \(a_{ij}=0\) for \(i\ne j\); scalar matrix: \(a_{ij}=0\) for \(i\ne j\), \(a_{11}=a_{22}=\cdots=a_{nn}=k\); identity matrix: scalar matrix with \(k=1\); upper triangular: \(a_{ij}=0\) for \(i>j\); lower triangular: \(a_{ij}=0\) for \(i<j\).

Variables: \(a_{ij}\): entries of the matrix.

Conditions: As stated for each type.

Recognition and use of structural properties.