Exercise 1.2 - Chapter 1 - Matrices and Determinants - 11th Business Maths Guide Samacheer Kalvi Solutions

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Exercise 1.2

1.2 Text Book Back Questions and Answers

Question 1.
Find the adjoint of the matrix A =

Solution:

Question 2.

If A =

 then verify that A(adj A) = |A| I and also find A^-1.
Solution:

Given A =

From (1) and (2), A(Adj A) = |A| I

Question 3.
Find the inverse of each of the following matrices:

Solution:

Question 4.
If A = and B = , then verify adj(AB) = (adj B) (adj A).
Solution:

From (1) and (2), adj (AB) = (adj B) (adj A)

Question 5.
If A =   then, show that (adj A) A = O.

Solution:

Question 6.
If A =  then, show that the inverse of A is A itself.
Solution:

∴ A^-1 = A
Hence proved.

Question 7.
If A^-1 =   then, find A.
Solution:

Given A^-1 = 

We know that (A^-1)^-1 = A
So we have to find inverse of A^-1

Question 8.
Show that the matrices A =  and B =   are inverses of each other.
Solution:
To prove that A and B are inverses of each other.
We have to prove that AB = BA = I.

Thus AB = BA = I
Hence A and B are inverses of each other.

Question 9.
If A =   and B =  , then verify that (AB)^-1 = B^-1A^-1

Solution:

Now we will find B^-1A^-1

From (1) and (2), (AB)^-1 = B^-1A^-1

Question 10.
Find λ if the matrix   has no inverse.

Solution:

1[11λ – 28] – 1[22 – 36] + 3[14 – 9λ] = 0
11λ – 28 + 14 + 42 – 27λ = 0
-16λ + 28 = 0
-16λ = -28

Question 11.

If X =   and Y =   then, find p, q if Y = X^-1
Solution:
Given that Y is the inverse of X.
∴ XY = I

6 – 3p = 0 and -9 – 3q = 0
6 = 3p and -9 = 3q
∴ p = 2; q = -3