Matrices and Determinants
Exercise 3.3
Question 1: Find the transpose of each of the following matrices:
Answer
Question 2:
Answer
We have
Question 3:
Answer
Question 4:
Question 5: For the matrices A and B, verify that (AB)′ = B'A' where
Question 6:
Answer
(ii)
Question 7:
Answer
Hence, A is a skewsymmetric matrix.
Question 8:
Answer
Question 9:
Answer
Question 10: Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
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:
Thus, (AB − BA) is a skewsymmetric matrix.
Question 12:
If if the value of α is
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