A square matrix [aij] such that aij=0 for i=j and aij=k where k is a constant for i=j is called

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A square matrix [ { a }_{ ij } ] such that { a }_{ ij }=0 for

Question

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

Diagonal as well as scalar matrix

Scalar matrix

Unit matrix

None of the above

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Asher Discussed

A square matrix

[a_{ij}]

such that

a_{ij} = 0

for

i \neq = j

and

a_{ij} = k

where

k

is a constant for

i = j

is called

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14 mins ago

Text solutionVerified

By given, we can construct a matrix as below

= ⎣ ⎡ k 0 ... 00 0 k ... .. 0 ... .. .. 0 ... 0 .. .. k 0 00 .. 0 k ⎦ ⎤

Clearly the matrix is a diagonal matrix as all non diagonal elements are zero.
Also, the matrix is also a scalar matrix because all diagonal elements are same and non diagonal elements are zero.
So, option A is correct.

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Question Text	A square matrix $[a_{ij}]$ such that $a_{ij} = 0$ for $i \neq = j$ and $a_{ij} = k$ where $k$ is a constant for $i = j$ is called
Answer Type	Text solution:1
Upvotes	150

A square matrix [aij​] such that aij​=0 for i=j and aij​=k where k is a constant for i=j is called

Text solutionVerified

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