The Total solution for NCERT class 6-12
Find the inverse of each of the matrices (if itexists).
Answer - 11 : -
Let and. Verify that
Answer - 12 : -
From (1) and (2), we have:
(AB)−1 = B−1A−1
Hence, the given result is proved.
If, show that. Hence find.
Answer - 13 : -
For the matrix, find the numbers a and b suchthat A2 + aA + bI = O.
Answer - 14 : -
We have:
Comparing the corresponding elements of the twomatrices, we have:
Hence, −4 and 1 are the required values of a and b respectively.
For the matrixshow that A3 −6A2 + 5A + 11 I = O. Hence,find A−1.
Answer - 15 : -
From equation (1), we have:
If verify that A3 −6A2 + 9A − 4I = O andhence find A−1
Answer - 16 : -
Let A be a nonsingular squarematrix of order 3 × 3. Then is equal to
Answer - 17 : -
A. B. C. D.
Solution
We know that,
Hence, the correct answer is B.
If A is an invertible matrix oforder 2, then det (A−1) is equal to
Answer - 18 : -
A. det (A) B. C. 1 D. 0
Since A is an invertiblematrix,