Question

In an upper triangular matrix $A={\left[a_{ij}\right]}_{n\times n}$ the elements $a_{ij}=0$ for

• A. $i$
• B. $i=j$
• C. $i>j$
• D. $i\le j$

Answer 1

The correct option is C $i>j$

A is an upper triangle then $A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \dots .& a_{1n}\\ 0& a_{22}& ....& a_{2n}\\ ....& ....& ....& ....\\ 0& 0& ....& a_{nn}\end{array}\right]$

$\therefore a_{21}=0,a_{31}=\mathrm{0......}{a}_{n1}=0$

$a_{32}=0,a_{42}\dots ..a_{n2}=0$ and so on

$\therefore a_{ij}=0$ for $i>j$.