Mathematics Quick Revision of Matrix For CBSE-NCERT
Click for Only Video

### Matrix

\color{green} ✍️ A matrix is an ordered rectangular array of numbers or functions.

\color{green} ✍️ A matrix having m rows and n columns is called a matrix of order m × n

### Types of matrix

If any matrix [b_(ij)]_(mxxn)

● Row matrix color{red}{=> m =1}
●Column matrix color{red}{=> n=1}
●Square matrix color{red}{=> m=n}

●Diagonal matrix color{red}{=> b_(ij) = 0; \ \ i ne j}

●Scalar matrix color{red}{=> b_(ij) = 0; \ \ i ne j \ \ "and" b_(ij) = k; \ \ i=j }

●Identity matrix color{red}{ => b_(ij) = 0; \ \ i ne j \ \ "and" b_(ij) = 1; \ \ i=j }

●Zero matrix color{red}{=> b_(ij) = 0}

### Algebra of matrices

● Euality of matrix :
color{blue}{A = B =>[a_(ij)] = [b_(ij)]}

color{blue}{A + B =>[a_(ij)] + [b_(ij)]}

● Substraction of matrix :
color{blue}{A - B =>[a_(ij)] - [b_(ij)]}

### Multiplication by scalar and matrix multiplication

Multiplication by scalar :

k [a_(ij)]_(mxxn) = [ka_(ij)]_(mxxn)

Matrix Multiplication =>

### Transpose and its properties

=> Transpose color{red}{A = [a_(ij)]_(m × n)}, then color{blue}{A′ = A^T= [a_(ji)]_(n × m)}.

Properties of transpose :

(i) (A′)′ = A,
(ii) (kA)′ = kA′ (where k is any constant)
(iii) (A + B)′ = A′ + B′
(iv) (A B)′ = B′ A′

### Symmetric and Skew Symmetric Matrices

color{blue}{"Symmetric Matrix :"}

\color{green} ✍️ A square matrix A = [a_(ij)] is said to be symmetric

color{red}{"If "A′ = A, \ \ "that is,"\ \ [a_(ij)] = [a_(ji)]} for all possible values of i and j.

color{blue}{"Skew Symmetric Matrix :"}

\color{green} ✍️ A square matrix A = [aij] is said to be skew symmetric matrix

color{red}{"if" A′ = – A,\ \ "that is" \ \ a_(ji) = – a_(ij) for all possible values of i and j.

### Elemetry transformation

Example of Row transformation :