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Chapter 4 Determinants Ex 4.5 Solutions

Question - 11 : -

Find the inverse of each of the matrices (if itexists).

Answer - 11 : -

Question - 12 : -

Let and. Verify that 

Answer - 12 : -


From (1) and (2), we have:

(AB)−1 = B−1A−1

Hence, the given result is proved.

Question - 13 : -

If, show that. Hence find.

Answer - 13 : -


Question - 14 : -

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.

Question - 15 : -

For the matrixshow that A3 −6A2 + 5A + 11 I = O. Hence,find A−1.

Answer - 15 : -


From equation (1), we have:

Question - 16 : -

If verify that A3 −6A2 + 9A − 4I = O andhence find A−1

Answer - 16 : -


From equation (1), we have:

Question - 17 : -

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.

Question - 18 : -

If A is an invertible matrix oforder 2, then det (A−1) is equal to

Answer - 18 : -

A. det (AB.  C. 1 D. 0

Solution

Since A is an invertiblematrix, 

Hence, the correct answer is B.

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