Determinants
Exercise 4.5
Question 1: Find adjoint of each of the matrices.
Answer
Question 2: Find adjoint of each of the matrices.
Answer
Question 3:
Answer
Question 4:
Answer
Question 5: Find the inverse of each of the matrices (if it exists).
Answer 5:
Question 6: Find the inverse of each of the matrices (if it exists).
Answer
Question 7: Find the inverse of each of the matrices (if it exists).
Answer
Question 8: Find the inverse of each of the matrices (if it exists).
Answer
Question 9: Find the inverse of each of the matrices (if it exists).
Answer
Question 10: Find the inverse of each of the matrices (if it exists).
Answer
Question 11: Find the inverse of each of the matrices (if it exists).
Answer
Question 12:
Let . Verify that (AB)^{1 = }B^{1}A^{1}
Answer
From (1) and (2), we have:
(AB)^{−1} = B^{−1}A^{−1}
Hence, the given result is proved.
Question 13:
If show that Hence find A^{1}.
Answer
Question 14:
For the matrix , find the numbers a and b such that A^{2} + aA + bI = O.
Answer
Hence, −4 and 1 are the required values of a and b respectively.
Question 15:
For the matrix show that A^{3} − 6A^{2} + 5A + 11 I = O. Hence, find
A^{−1}.
Answer
Question 16:
If verify that A^{3} − 6A^{2} + 9A − 4I = O and hence find A^{−1}
Answer
From equation (1), we have:
Question 17:
Answer B
Hence, the correct answer is B.
Question 18: If A is an invertible matrix of order 2, then det (A^{−1}) is equal to
Answer
B. C. D.
Hence, the correct answer is B.
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