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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 A^T 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:

Question 9.

Solution:
A + 2B + 3C

Question 10.

Solution:


From (i) and (ii), we get

Question 11.

Solution:

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

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.