If a_ ij =0 (i j ) and _ ij =2 (i= j ) then the matrix A= [ a_ ij… - Vidyadip

MCQ

If $\displaystyle \text{a}_{\text{ij}}=0\left (\text{i}\neq \text{j} \right )$ and $\displaystyle\text{a}_{\text{ij}}=2\left (\text{i= j} \right )$ then the matrix $\text{A}=\displaystyle \left [ \text{a}_{\text{ij}} \right ]_{\text{n}\times\text{n}}$ is a $ ........ $ matrix ?

A
unit
B
null
✓
scalar
D
skew symmetric

✓

Answer

Correct option: C.

scalar

Given $A$ is a square matrix as the number of rows and columns are same as $n$
The elements $\text{a}_\text{ij}$ where $\text{i} = \text{j} $ lie along the diagonal.
and the elements $\text{a}_\text{ij}$ where $\text{i}\neq\text{j}$ do not lie along the diagonal.
Given, diagonal elements $= 2$ and the rest of the elements $= 0$
Such a diagonal matrix where all diagonal elements are equal, is called a scalar matrix.

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