A square matrix [a_i j ] such that a_i j=0 for i ≠ j and a_i j=k where k is a constant for i=j is called :

Correct answer: (B) scalar matrix. In a scalar matrix, a_i j= \ 0 for i ≠ j k for i=j . Example [ 4 0 0 0 4 0 0 0 4 ]

Q178 / 270 · NDA 2012 (Phase 2) · Mathematics

A square matrix $\left[a_{i j}\right]$ such that $a_{i j}=0$ for $i \neq j$ and $a_{i j}=k$ where $k$ is a constant for $i=j$ is called :

A
diagonal matrix, but not scalar matrix
Correct answer
B
scalar matrix
C
unit matrix
D
None of the above

Solution

In a scalar matrix, $a_{i j}=\left\{\begin{array}{lll}0 & \text { for } \quad i \neq j \\ k & \text { for } \quad i=j\end{array}\right.$ Example $\left[\begin{array}{lll}4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4\end{array}\right]$

Hence, the correct answer is option: 'B'.

A square matrix $\left[a_{i j}\right]$ such that $a_{i j}=0$ for $i \neq j$ and $a_{i j}=k$ where $k$ is a constant for $i=j$ is called :

Solution

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