Plus Two Math's Solution Ex 3.3 Chapter 3 Matrices | Kerala Notes

Plus Two Math's Solution Ex 3.3 Chapter3 : Matrices

Discover how to improve your maths grades with our high-quality, easy-to-understand maths textbook solutions. Our solutions are packed with information to ensure you get the best out of your studying Here is the solution for Exercise 3.3 Chapter 3 Matrices of NCERT plus two maths. Here we have given a detailed explanation of each and every exercise so that students can understand the concepts easily without any difficulty. The solution to each and every question is provided here so you can solve them by yourself if you don’t get the answer here.

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BoardSCERT, Kerala
Text BookNCERT Based
ClassPlus Two
SubjectMath's Textbook Solution
ChapterChapter 3
ExerciseEx 3.3
Chapter NameMatrices
CategoryPlus Two Kerala


Kerala Syllabus Plus Two Math's Textbook Solution Chapter  3 Matrices Exercises 3.3


Chapter 3  Matrices Solution



Kerala plus two maths NCERT textbooks, we provide complete solutions for the exercise and answers provided at the end of each chapter. We also cover the entire syllabus given by the Board of secondary education, Kerala state.

Chapter 3  Matrices Exercise   3.3

Find and, when 

The given matrix is


Find the transpose of each of the following matrices:

(i)  (ii)  (iii)  

(i) (ii) (iii) 


If and, then verify that

(i) 

(ii) 

We have:

(i)

(ii)


If and, then verify that

(i) 

(ii) 

(i) It is known that

Therefore, we have:

(ii)


If and, then find 

We know that


For the matrices A and B, verify that (AB)′ =  where

(i) 

(ii) 

(i)

(ii)


If (i) , then verify that 

(ii) , then verify that 

(i)

(ii)


(i) Show that the matrix is a symmetric matrix

(ii) Show that the matrix is a skew symmetric matrix.

(i) Transpose of a matrix is equal to original matrix,then it is symmetric.                           

Hence, A is a symmetric matrix.

(ii) If it is equal to negetive,then it is skew symmetric matrix. Diagonal elements of this matrix are zero.

Hence, A is a skew-symmetric matrix.


For the matrix, verify that

(i)  is a symmetric matrix

(ii)  is a skew symmetric matrix

(i) 

Hence,  is a symmetric matrix.

(ii) 

Hence, is a skew-symmetric matrix.


Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(i) 

(ii) 

(iii) 

(iv) 

(i)

Thus,  is a symmetric matrix.

Thus,  is a skew-symmetric matrix.

Representing A as the sum of P and Q:

(ii)

Thus,  is a symmetric matrix.

Thus,  is a skew-symmetric matrix.

Representing A as the sum of P and Q:

(iii)

Thus,  is a symmetric matrix.

Thus,  is a skew-symmetric matrix.

Representing A as the sum of P and Q:

(iv)

Thus,  is a symmetric matrix.

Thus, is a skew-symmetric matrix.

Representing A as the sum of P and Q:


If AB are symmetric matrices of same order, then AB − BA is a

A. Skew symmetric matrix B. Symmetric matrix

C. Zero matrix D. Identity matrix

The correct answer is A.

A and B are symmetric matrices, therefore, we have:

Thus, (AB − BA) is a skew-symmetric matrix


If, then, if the value of α is

A.  B. 

C. π D. 

The correct answer is B.

Comparing the corresponding elements of the two matrices, we have:




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Chapter 3: Matrices Exercise 3.3 Textbook Solution


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