Chapter 4 Determinants and Matrices Ex 4.7

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Chapter 4 Determinants and Matrices Ex 4.7

Chapter 4 Determinants and Matrices Ex 4.7

Question 1.

Question 2.


∴  = -A and A = –
∴ A and AT both are skew-symmetric matrices.

Question 3.

Solution:

Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 2
From (i) and (ii), we get
(2A = 2

Question 4.

Solution:

From (i) and (ii), we get
(3A = 3

Question 5.

Solution:

Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 4

Question 6.

Solution:

Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 5
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
Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 7

Question 8.

Solution:

Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 8

Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 9

Question 9.

Solution:

A + 2B + 3C

Question 10.

Solution:


Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 12
From (i) and (ii), we get

Question 11.

Solution:



Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 14
Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 15

Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 16
Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 17

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 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 19

Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 20

Question 13.

Solution:


Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 22
From (i) and (ii), we get


From (i) and (ii) we get

Question 14.

Solution:

Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 24
Maharashtra Board 11th Maths Solutions Chapter 4 Determinants and Matrices Ex 4.7 25
∴ A = I, where I is the unit matrix of order 2.