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

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Board	SCERT, Kerala
Text Book	NCERT Based
Class	Plus Two
Subject	Math's Textbook Solution
Chapter	Chapter 3
Exercise	Ex 3.3
Chapter Name	Matrices
Category	Plus Two Kerala

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

Chapter 3  Matrices Solution

• Exercises 3.1
• Exercises 3.2
• Exercises 3.3
• Exercises 3.4
• Miscellaneous Exercise Chapter 3
•  

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

Question 1:

Find and, when 

Solution 1:

The given matrix is

Question 2:

Find the transpose of each of the following matrices:

(i)  (ii)  (iii)  

Solution 2:

(i) (ii) (iii) 

Question 3:

If and, then verify that

(i) 

(ii) 

Solution 3:

We have:

(i)

(ii)

Question 4:

If and, then verify that

(i) 

(ii) 

Solution 4:

(i) It is known that

Therefore, we have:

(ii)

Question 5:

If and, then find 

Solution 5:

We know that

Question 6:

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

(i) 

(ii) 

Solution 6:

(i)

(ii)

Question 7:

If (i) , then verify that 

(ii) , then verify that 

Solution 7:

(i)

(ii)

Question 8:

(i) Show that the matrix is a symmetric matrix

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

Solution 8:

(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.

Question 9:

For the matrix, verify that

(i)  is a symmetric matrix

(ii)  is a skew symmetric matrix

Solution 9:

(i) 

Hence,  is a symmetric matrix.

(ii) 

Hence, is a skew-symmetric matrix.

Question 10:

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

(i) 

(ii) 

(iii) 

(iv) 

Solution 10:

(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:

Question 11:

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

A. Skew symmetric matrix B. Symmetric matrix

C. Zero matrix D. Identity matrix

Solution 11:

The correct answer is A.

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

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

Question 12:

If, then, if the value of α is

A.  B. 

C. π D. 

Solution 12:

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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Plus Two Math's Chapter Wise Textbook Solution PDF Download

            Plus Two Math's Part I

• Chapter 1: Relations and Functions
• Chapter 2: Inverse Trigonometric Functions
• Chapter 3: Matrices
• Chapter 4: Determinants
• Chapter 5: Continuity and Differentiability
• Chapter 6: Application of Derivatives



             Plus Two Math's Part II

• Chapter  7: Application of Integrals
• Chapter  8: Integrals
• Chapter  9: Differential Equations
• Chapter 10: Vector Algebra
• Chapter 11: Three Dimensional Geometry
• Chapter 12: Linear Programming
• Chapter 13: Probability

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