RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 7. Adjoint and Inverse of a Matrix

Subject: Maths - Class 12th

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Exercise 7

1

Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.
2

Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.
3

Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.
4

Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.
5

Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.
6

Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.
7

Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.
8

Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.
9

Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.
10

If A = , show that adj A = A.
11

If A = , show that adj A = 3A’.
12


13

Find the inverse of each of the matrices given below.
14

Find the inverse of each of the matrices given below.
15

Find the inverse of each of the matrices given below.

, when (ab – bc) 0
16

Find the inverse of each of the matrices given below.
17

Find the inverse of each of the matrices given below.
18

Find the inverse of each of the matrices given below.
19

Find the inverse of each of the matrices given below.
20

Find the inverse of each of the matrices given below.
21

Find the inverse of each of the matrices given below.
22

If A = , show that A-1 = A.
23

If A = , show that A-1 = A2.
24

If A = , prove that A-1 = A3.
25

If A = show that A-1= A’.
26

Let D = diag [d1, d2, d3], where none of d1, d2, d3 is 0; prove that D-1 = diag [d1-1, d2-1, d3-1].
27

If A = and B = , verify that (AB)-1 = B-1 A-1.
28

If A = and B = , verify that (AB)-1 = B-1 A-1.
29

Compute (AB)-1 when A = and B-1 -= .
30

Obtain the inverses of the matrices and . And, hence find the inverse of the matrix .
31

If A = , verify that A2 – 4A – I = O, and hence find A-1.
32

Show that the matrix A = satisfies the equation

33

If A = , show that A2 + 3A + 4I2 = O and hence find A-1.
34

If A = , find

35

If A = . Find the value of λ so that A2 = λA – 2I. Hence, find A-1.

[CBSE 2007]
36

Show that the A = satisfies the equation A3 – A2 – 3A – I = O, and hence find A-1.
37

Prove that: (i) adj I = I (ii) adj O = O (iii) I-1 = I.