# Matrices For Class 12

Matrix is an important branch of Mathematics.  It is one of the most powerful tools, which has various application such as in solving linear equations, in budgeting, sales projection, cost estimation, etc. Matrices for class 12 covers the important concepts in matrices, such as types, order, matrix elementary transformation operations and so on. Students can get a detailed explanation of matrix concepts here. Matrices for class 12 helps the students for their higher studies, as it covers all the basic topics. Go through the notes on class 12 matrices to score good marks in the examinations.

## Matrices for Class 12 Topics

The topics covered in matrices for class 12 include the following topics:

• Matrix Introduction
• Types
• Operations
• Transpose of a Matrix
• Symmetric and Skew Symmetric Matrix
• Elementary Operations of a Matrix (Transformations)
• Invertible Matrices

## Matrices Definition

A matrix is a function which consists of an ordered rectangular array of numbers. The numbers in the array are called the entities or the elements of the matrix. The horizontal array of elements in the matrix is called rows, and the vertical array of elements are called the columns. If a matrix has m rows and n columns, then it is known as the matrix of order m x n.

## Types of Matrices

Depending upon the order and elements, matrices are classified as,

### Column Matrix

A column matrix is an m × 1 matrix, consisting of a single column of m elements. It is also called a column vector.

### Row Matrix

A row matrix is a 1 × m matrix, consisting of a single row of m elements. It is also called a row vector.

### Square Matrix

A matrix which has an equal number of rows and columns. It is expressed as m × m.

### Diagonal Matrix

A matrix which has non-zero elements in its diagonal part running from upper left to the lower right or vice versa.

### Scalar Matrix

The scalar matrix is a square matrix, which has all its diagonal elements equal and all the off-diagonal elements as zero.

### Identity Matrix

A square matric which has all its principal diagonal elements as ones and all non-diagonal elements as zeros.

### Zero Matrix

A matrix whose all entries are zero. It is also called a null matrix.

### Equality of Matrices

Two matrices are said to be equal if-

(i) The order of both the matrices are the same

(ii) Each element of one matrix is equal to the corresponding element of the other matrix.

### Matrices for Class 12 Examples

Example:

If $\begin{bmatrix} x+3 & z+4 & 2y-7\\ -6 & a-1 & 0\\ b-3 & -21 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 6 & 3y-2 \\ -6 & -3 & 2c +2\\ 2b+4 & -21 & 0 \end{bmatrix}$, then find the value of a, b, c, x, y, and z.

Solution:

It is given that, the two matrices are equal. Therefore, the corresponding elements present in matrices should be equal to each other. By comparing the corresponding elements in the matrices, we get:

x+3 = 0.

⇒  x = -3

z +4 = 6

⇒ z = 6-4

⇒ z = 2

2y-7 = 3y-2

⇒3y-2y =-7+2

⇒y = -5

a-1 = -3

⇒a = -3+1

⇒a=-2

2c+2 = 0

⇒2c = -2

⇒ c = -1

b-3 = 2b+4

⇒2b-b = -3-4

⇒ b = -7

Therefore, the values of the variables are:

a = -2

b = -7

c = -1

x = -3

y = -5

z = 2