ML Aggarwal ISC Matrices Class-12 Understanding APC Mathematics Solutions Chapter-3. Step by step Solutions of ML Aggarwal ISC Understanding APC Mathematics Class-12  Exercise 3.1, Exe 3.2 And Exe 3.3, Exe 3.4, Exe 3.5 With Chapter Test Questions. Visit official Website for detail information about ISC Board Class-12 Mathematics.

## ML Aggarwal ISC Matrices Class-12 Maths APC Ch-3

 Class: 12th Subject: Mathematics Chapter  : Ch-3 Matrices Page-166 to 218
 Board ISC Writer ML Aggarwal ISC Understanding Vol-I Publications APC Arya Publications

-: Select Topics :-

Exe-3.1,

Exe-3.2,

Exe-3.4,

Exe-3.5,

Chapter Test

### ML Aggarwal ISC Matrices Class-12 Maths APC Ch-3

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 a 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 matrix which has all its principal diagonal elements as 1’s 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

Exe-3.1

### ISC Matrices Class-12 Maths APC Ch-3

Page-166, 167

Question 1:

If a matrix of type …………………. as a matrix ?

Question 2:
If a column matrix ……………………….. row of A ?

Question 3:

…………………

…………………

………………..

Question 13:

Find x, y, a and b if ………………………. .

### Exe-3.2

ML Aggarwal Matrices Class-12 Maths APC Ch-3

Page-174, 175

Question 1:

If A = …………………. find the following :

……………..

……………….

Question 2:

Compute the following :

………………..

…………………

………………

Question 18:

If A = ………………. 2A + 3x = 5B .

Exe-3.3

### ML Aggarwal ISC Matrices Class-12 Maths APC Ch-3

Page-192, 193, 194, 195

Question 1:

(i) write the order  of the product matrix ……….

(ii) If A …………….

Question 2:

(i) If A ……………..

(ii) If A is a matrix ……………

Question 3:

…………………….

…………………….

……………………..

Question 37:

Find the matrix A such that …………..

Question 38:

Find the matrix A such that …………..

### Exe-3.4

ML Aggarwal ISC Class-12 Maths APC Ch-3

Page-207, 208

Question 1:

If A = ………………….. then find (3A).

Question 2:

If A = …………… find A’ + B’.

Question 3:

……………………

…………………..

……………………

Question 28:

Express the following matrixes as the sum of the symmetric and skew symmetric matrices :

………………….

Exe-3.5

### ML Aggarwal ISC Matrices Class-12 Maths APC Ch-3

Page-216

Question 1:

Use elementary  column operation …………….. matrix equations :

Find the inverse of the following matrices .If they exits, by using elementary operations :

Question 2:

……………..

……………….

……………….

Question 5:

Using elementary row operation , find the inverse of the following matrices

…………..

### Chapter Test

ISC Matrices Class-12 Maths APC Ch-3

Page-217

Question 1:

(i) Construct a 2 x 3 matrix ……….

(ii) Construct a 2 x 4 matrix ……….

Question 2:

Construct a 2 x 3 matrix A = ………………… greatest integer number.

Question 3:

…………………….

…………………..

……………………..

Question 19:

If M = …………………. M.

(i) Prove that * is a binary  operation on M.

(ii) Prove that ……………..

(iii)  Find the identity …………………

-: End of Matrices  ML Aggarwal Vol-I ISC Class-12 Solutions:-

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