CBSE Class 12 Mathematics NCERT Exemplar Solutions: Chapter - Matrices

Here we are providing NCERT Exemplar Solutions for all the questions of Class 12 Mathematics Chapter 3 – Matrices. These questions are solved by experienced subject experts of Mathematics in the most appropriate and simple way so as to help students access the right source for the exam preparation. The questions given in the chapter Matrices of NCERT Exemplar Solutions are very important for board exams as well as engineering entrance exams like JEE Main, WBJEE and UPSEE etc.

Important Topics of Chapter – Matrices

• Notation and order of matrix,
• Addition, subtraction and multiplication of matrices,
• Equality of matrix,
• Types of matrix like diagonal, zero and identity matrix etc.,
• Transpose of a matrix,
• Symmetric and skew symmetric matrices and
• Invertible matrices
• Proof of the uniqueness of inverse, if it exists

Few problems along with their solutions from this chapter are given follows:

Question:

Total number of possible matrices of order 3 x 3 with each entry 2 or 0 is

(a) 9    

(b) 27  

(c) 81  

(d) 512

Solution: (d)

Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is 2⁹ i.e., 512.

Question:

If A and B are two matrices of the order 3 × m and 3 × n, respectively and m = n, then order of matrix (5A - 2B) is

(a) m × 3                     

(b) 3 × 3                     

(c) m × n                     

(d) 3 × n

Solution: (d)     

We are given that, the order of the matrices A and B are 3 × m and 3 × n respectively. Now, If m = n, then A and B have same orders as 3 × n each, so the order of (5A – 2B) should be same as 3 × n.

Question:

The negative of a matrix is obtained by multiplying it by

Solution:           

Let A be a matrix of any order.

We can find the negative of A by multiplying all the elements of A by -1 i.e., -A = -1[A]

Thus, the negative of a matrix is obtained by multiplying it by  -1.

Question:

A matrix which is not a square matrix is called a………..matrix.

Solution:           

If the number of rows and columns of a matrix are not same, then the matrix is known as a rectangular matrix. Thus, a matrix which is not a square matrix is called a rectangular matrix.

Question:

In applying one or more row operations while finding A^-1 by elementary
row operations, we obtain all zeroes in one or more, then A^-1 .......  .

Solution:           

In applying one or more row operations while finding A^-1 by elementary row operations, we obtain all zeroes in one or more, then A^-1 does not exist.

Question:

Matrices of any order can be added.

Solution: False

The necessary condition for addition of two matrices is that both the matrices are of the same order.

Question:

Matrix addition is associative as well as commutative.

Solution: True

Consider, A, B and C are matrices of same order.

Associative property of Matrix addition:

(A + B) + C = A + (B + C)

Commutative property of Matrix addition:

A + B = B + A

Question:

If matrix AB = 0, then A = 0 or B = 0 or both A and B are null matrices.

Solution: False

Since, for two non-zero matrices A and B of same order, it can be possible that A × B = 0 = null matrix

Students can download the complete solutions in PDF form using the links given below:

About NCERT Exemplar Book Class 12 Maths:

To score maximum marks in board exams, students must practice the questions given in NCERT Exemplar Book published by NCERT. The questions are also important for engineering entrance exams as the level of these questions matches the difficulty level of the questions generally asked in engineering entrance exams. Each chapter of NCERT Exemplar Class 12 Maths book starts with a brief overview of the chapter followed by solved examples and unsolved exercises.

Importance of NCERT Exemplar Books:

• All NCERT Exemplar books are written in an easy language by experienced teachers and professor having deep knowledge and understanding of the subject.
• With the help of NCERT Exemplar books, students can easily understand the basics and fundamentals of any topic.
• All NCERT books contain standard questions plus some extra information for competitive exams.
• Many questions in JEE-Main and Board exams are directly asked from NCERT Exemplar books

In this chapter of the book, students will get the following things.

• Brief summary of the complete chapter
• Short answer type questions
• Long answer types questions
• Objective type questions or MCQs
• Fill in the blanks
• True and False

Students can download the complete NCERT Exemplar book from the link given below: