Question 1.
![Maharashtra Board Class 11 Maths Part 1 Chapter 4 Determinants and Matrices Ex 4.7 Solution 2 word image 17516 2](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17516-2.png)
Question 2.
∴ = -A and A = –
∴ A and AT both are skew-symmetric matrices.
Question 3.
Solution:
From (i) and (ii), we get
(2A = 2
Question 4.
Solution:
From (i) and (ii), we get
(3A = 3
Question 5.
Solution:
Question 6.
Solution:
From (i) and (ii), we get
[Note: The question has been modified.]
From (i) and (ii), we get
Question 7.
Solution:
3A – 2B + C = I
∴ C = I + 2B – 3A
Question 8.
Solution:
![Maharashtra Board Class 11 Maths Part 1 Chapter 4 Determinants and Matrices Ex 4.7 Solution 14 word image 17516 20](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17516-20.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 4 Determinants and Matrices Ex 4.7 Solution 15 Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 9](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/maharashtra-board-11th-maths-solutions-chapter-4-d-89.png)
Question 9.
Solution:
A + 2B + 3C
Question 10.
Solution:
From (i) and (ii), we get
Question 11.
Solution:
![Maharashtra Board Class 11 Maths Part 1 Chapter 4 Determinants and Matrices Ex 4.7 Solution 26 Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 16](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/maharashtra-board-11th-maths-solutions-chapter-4-d-93.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 4 Determinants and Matrices Ex 4.7 Solution 27 word image 17516 36](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17516-36.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 4 Determinants and Matrices Ex 4.7 Solution 28 Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 17](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/maharashtra-board-11th-maths-solutions-chapter-4-d-94.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 4 Determinants and Matrices Ex 4.7 Solution 29 word image 17516 38](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17516-38.png)
Question 12.
Express the following matrices as the sum of a symmetric and a skew symmetric matrix.
Solution:
A square matrix A can be expressed as the sum of a symmetric and a skew symmetric matrix as
![Maharashtra Board Class 11 Maths Part 1 Chapter 4 Determinants and Matrices Ex 4.7 Solution 34 Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 20](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/maharashtra-board-11th-maths-solutions-chapter-4-d-96.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 4 Determinants and Matrices Ex 4.7 Solution 35 word image 17516 45](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-17516-45.png)
Question 13.
Solution:
From (i) and (ii), we get
From (i) and (ii) we get
Question 14.
Solution:
∴ A = I, where I is the unit matrix of order 2.