to identify a square matrix A = (aij) where aij = 0 for all i j.

Question

to identify a square matrix A = (aij) where aij = 0 for all i > j.

ScanSolve AI Tutor · Accepted Answer

The question asks to identify a square matrix $A = (a_{ij})$ where $a_{ij} = 0$ for all $i > j$ .

Understand the condition $a_{ij} = 0$ for $i > j$ .
In a matrix, $i$ represents the row number and $j$ represents the column number. The condition $i > j$ means that the row number is greater than the column number. These elements are located below the main diagonal of the matrix. So, the condition states that all elements below the main diagonal are zero.
Review the definitions of the given matrix types.
- An upper triangular matrix is a square matrix where all elements below the main diagonal are zero. That is, $a_{ij} = 0$ for $i > j$ .
- A lower triangular matrix is a square matrix where all elements above the main diagonal are zero. That is, $a_{ij} = 0$ for $i < j$ .
- An idempotent matrix is a square matrix $A$ such that $A^2 = A$ .
- An identity matrix is a square matrix where all diagonal elements are 1 and all non-diagonal elements are 0.
Match the condition to the correct definition.
The given condition, $a_{ij} = 0$ for all $i > j$ , perfectly matches the definition of an upper triangular matrix.

The correct option is A.

A. Upper triangular matrix

To identify a square matrix A = (aij) where aij = 0 for all i > j.