NCERT Solutions, Matrices, Part -3, Class 12, Maths Notes - Class 12

Class 12: NCERT Solutions, Matrices, Part -3, Class 12, Maths Notes - Class 12

The document NCERT Solutions, Matrices, Part -3, Class 12, Maths Notes - Class 12 is a part of Class 12 category.
All you need of Class 12 at this link: Class 12

Matrices and Determinants


Exercise 3.3
Question 1: Find the transpose of each of the following matrices:
matrices, mathematics, Question and Answer (Q & A)


Answer
matrices, mathematics, Question and Answer (Q & A)

 
Question 2:
matrices, mathematics, Question and Answer (Q & A)


Answer

We have

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


Question 3:

matrices, mathematics, Question and Answer (Q & A)

Answer
matrices, mathematics, Question and Answer (Q & A)matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


Question 4:
matrices, mathematics, Question and Answer (Q & A)


Question 5: For the matrices A and B, verify that (AB)′ = B'A' where
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


Question 6:

matrices, mathematics, Question and Answer (Q & A)


Answer
matrices, mathematics, Question and Answer (Q & A)


(ii)

matrices, mathematics, Question and Answer (Q & A)
matrices, mathematics, Question and Answer (Q & A)


Question 7:
matrices, mathematics, Question and Answer (Q & A)
Answer
matrices, mathematics, Question and Answer (Q & A)
matrices, mathematics, Question and Answer (Q & A)
Hence, A is a skew-symmetric matrix.


Question 8:
matrices, mathematics, Question and Answer (Q & A)
 

Answer
matrices, mathematics, Question and Answer (Q & A)

 

Question 9:
matrices, mathematics, Question and Answer (Q & A)

 

Answer

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

Question 10: Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)
matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)


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


Answer
The correct answer is A.
A and B are symmetric matrices, therefore, we have:

matrices, mathematics, Question and Answer (Q & A)
Thus, (AB − BA) is a skew-symmetric matrix.


Question 12:
If 
matrices, mathematics, Question and Answer (Q & A) if the value of α is

matrices, mathematics, Question and Answer (Q & A)

matrices, mathematics, Question and Answer (Q & A)

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