Let’s learn the different types of matrices

 

Column matrices

A column matrix only has 1 column

Example  

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Example

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So, column matrix is of the order m × 1

We write it as

  A = [a ij ] m × 1

 

Row matrices

A row matrix only has 1 row

 

Example

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So, row matrix is of the order 1 × n

We write it as

  A = [a ij ] 1 × n

 

Square matrix

A square matrix has equal number of rows & columns

 

Example

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So, a square matrix is of the order m × m

We write it as

  A = [a ij ] m × m

 

Diagonal matrix

In A diagonal matrix, the non-diagonal of element are zero.

A diagonal matrix is possible only in a square matrix

 

Example

27.jpg

 

So, in a diagonal matrix

  • It is should be a square matrix
  • Non-diagonal elements are 0

Scalar matrix

A scalar matrix is a diagonal matrix where diagonal elements are equal

 

Example

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So, in a scalar matrix

  • It is a square matrix
  • Non diagonal elements are 0
  • Diagonal elements are equal

Identity matrix

An identity matrix is a diagonal matrix where all diagonal elements are 1

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So, in a Identity matrix

  • It is a square matrix
  • Non diagonal elements are 0
  • All diagonal elements are 1

Note : An identity matrix is a scalar matrix

 

  1. Chapter 3 Class 12 Matrices
  2. Concept wise

Transcript

[โ– 8(5@9@3@๐‘ฆ@tan^(โˆ’1)โก๐‘ฅ )]_(5 ร— 1) [โ– 8(3@9@5)]_(3 ร— 1) [โ– 8(5@2@9@8)]_(4 ร— 1) [โ– 8(3&2@1&4)]_(2 ร—2) [โ– 8(9&5&2@1&8&5@3&1&6)]_(3 ร— 3) [โ– 8(๐‘ฅ&๐‘ฆ&๐‘ง&1@๐‘Ž&๐‘&๐‘&1@๐‘&๐‘ž&๐‘Ÿ&1@๐‘š&๐‘›&๐‘œ&1)]_(4 ร—4) Example Diagonal Elements Diagonal Elements [โ– 8(โˆ’1&0&0@0&2&0@0&0&3)]_(3 ร— 3) Diagonal Element [4]_(1 ร—1) [โ– 8(โˆ’1&0@0&โˆ’1)]_(2 ร—2) [โ– 8(3&0&0@0&3&0@0&0&3)]_(3 ร— 3) [4]_(1 ร— 1) I = [1]_(1 ร— 1) I =[โ– 8(1&0@0&1)]_(2 ร—2) I =[โ– 8(1&0&0@0&1&0@0&0&1)]_(3 ร— 3)

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.