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NCERT solution class 12 chapter 4 Determinants exercise 4.5 mathematics part 1

EXERCISE 4.5


Page No 131:

Question 1:

Find adjoint of each of the matrices.

Answer:

Question 2:

Find adjoint of each of the matrices.

Answer:

Question 3:

Verify A (adj A) = (adj AA = I .

Answer:

Question 4:

Verify A (adj A) = (adj AA = I .

Answer:

Page No 132:

Question 5:

Find the inverse of each of the matrices (if it exists).

Answer:

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 and. Verify that 

Answer:

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:

Question 14:

For the matrix, find the numbers a and b such that A2 + aA + bI O.

Answer:

We have:

Comparing the corresponding elements of the two matrices, 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:

From equation (1), we have:

Question 16:

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

Answer:

From equation (1), we have:

Question 17:

Let A be a nonsingular square matrix of order 3 × 3. Then  is equal to

A.  B.  C.  D. 

Answer:

Answer: B

We know that,

Hence, the correct answer is B.

Question 18:

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

A. det (AB.  C. 1 D. 0

Answer:

Since A is an invertible matrix, 

Hence, the correct answer is B.


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