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NCERT solution class 12 chapter 3 Matrices exercise 3.4 mathematics part 1

EXERCISE 3.4


Page No 97:

Question 1:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 2:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 3:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 4:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 5:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 6:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 7:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = AI

Question 8:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 9:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 10:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = AI

Question 11:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = AI

Question 12:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Now, in the above equation, we can see all the zeros in the second row of the matrix on the L.H.S.

Therefore, A−1 does not exist.

Question 13:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 14:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Applying, we have:

Now, in the above equation, we can see all the zeros in the first row of the matrix on the L.H.S.

Therefore, A−1 does not exist.

Question 15:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Question 16:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Applying R2 → R2 + 3R1 and R3 → R3 − 2R1, we have:

Question 17:

Find the inverse of each of the matrices, if it exists.

Answer:

We know that A = IA

Applying, we have:

Question 18:

Matrices A and B will be inverse of each other only if

A. AB = BA

C. AB = 0, BA = I

B. AB = BA = 0

D. AB = BA = I

Answer:

Answer: D

We know that if A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is said to be the inverse of A. In this case, it is clear that A is the inverse of B.

Thus, matrices A and B will be inverses of each other only if AB = BA = I.


 

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