# RS Aggarwal Class 12 Chapter 5 Solutions (Matrices)

RS Aggarwal Solutions for Class 12 Chapter 5 Matrices are prepared to help you solve the questions in a simple way. Matrices are an important mathematical tool which is used not only in sciences but also in the social sciences and management subjects. You will learn the definition of a matrix and various types of matrices such as row matrix, column matrix, square and diagonal matrices, scalar, identity, null; and upper and lower triangular matrices by practising the solution in RS Aggarwal Class 12 Solutions book.

There are 124 questions provided in 6 exercises with in-depth coverage of all topics in the CBSE and entrance exam syllabus. These exercise solutions are very reliable from the exam point of view and are of utmost importance. It is recommended that you practise the solutions well to stand out of the crowd among your peers. This chapter majorly covers the matrices, so you will become proficient in finding the addition, subtraction and products of different matrices after going through the detailed solutions for your reference.

Our subject matter experts are well aware of the doubts that you might encounter while solving the questions. Hence, we have prepared the well-researched solutions in line with the updated CBSE syllabus. You can use them as they are for practice and your Class 12 Board exams. Despite being detailed in nature, these answers will help you learn time management which is an important aspect for complex solutions.

## Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 5 Matrices

**Introduction:**

In this chapter, we will deeply study about Matrices. FYI, a set of numbers arranged in a rectangular form with m number of rows and n number of columns is known as an (m x n) Matrix.

A matrix may be represented as follows:

The matrix can be represented by A = [a_{ij}]_{m x n}

Please note a Matrix is generally used to represent a data set.

**Types of Matrices:**

Row Matrix: It is a matrix which has one row only.

Column Matrix: It is a matrix which has one column only.

Square Matrix: A matrix which has an equal number of rows and columns.

Diagonal Matrix: A square matrix in which all the elements apart from the main diagonal are zero, i.e., for a square matrix A = [aij]_{n x n,}

a_{ij} = 0 for all i ≠ j.

Scalar Matrix: Any square matrix, A = [a_{ij}]_{n x n }can be called as scalar if it meets the following criteria:

- a
_{ij}= 0 for all i ≠ j, and - a
_{ii}= C for all i, where C ≠ 0.

Identity/Unit Matrix: A diagonal matrix can be called an identity matrix if all elements of the main diagonal are 1.

Null Matrix: A matrix which has all its elements as zero.

Upper Triangular Matrix: A square matrix with all the elements below its main diagonal are zero is an upper triangular matrix.

Lower Triangular Matrix: A square matrix with all the elements above its main diagonal are zero is a lower triangular matrix.

**Operations on Matrices:**

Addition of Matrices: Two matrices of the same order can be added by adding their corresponding elements.

Multiplication of a Matrix by a Scalar: A matrix can be multiplied to a scalar by multiplying all the elements of the matrix with the scalar.

The difference of Matrices: A_{mxn} – B_{mxn}

The above can be solved by multiplying matrix B_{m x n} with (-1) and then adding the matrices.

Multiplication of Matrices: Two matrices A and B can only be multiplied if the number of columns of the first matrix (A) is equal to the number of rows of the second matrix

(B). A_{m x n }X B_{n x p}

The above can be solved by using the following formula:

**Transpose of a Matrix:**

The transpose of a matrix can easily be found by swapping the rows and columns of a matrix.

The transpose of a matrix A can be denoted by A’ or A^{T}.

If A=[a_{ij}]_{m x n} then,

A’ = [a_{ji}]_{n x m}.

**Symmetric and Skew Symmetric Matrices**

Symmetric Matrix: A matrix is called symmetric if it is equal to its transpose.

A’ = A

Skew Symmetric Matrix: A matrix is called skew-symmetric if its transpose is equal to the negative of the matrix.

A’ = – A

### Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 5 Matrices

- The exercise solutions in 5A are based on the identification of matrices, and the elements in its rows and columns as well as an understanding of drawing a given matrix.
- The exercise solutions in 5B are based mostly on the verification of various identities of Matrices.
- In the exercise 5C, you will learn to solve complicated function problems related to Matrices, you will also understand how to square a matrix.
- In exercise 5D, the transpose and the inverse of the matrices are discussed in the exercise solutions in detail.
- You will be required to find the inverse of the matrices using elementary row operations in the exercise 5E.
- The final exercise 5F will make you proficient in the matrices with a wide variety of miscellaneous problems.
- Solving these questions will bring you at ease with this topic, which is going to be useful throughout your higher studies, as well as in competitive exams.

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