Fsc Part 1 Mathematics (Complete Solution)

# Q2 Find the inverse of the following matrices

(i)

 3 -1 2 1

Solution:

Let     A=

 3 -1 1 1

Then A-1=
 Adj.A lAl
lAl=

 3 -1 1 1

=3+2 =5≠0
Adj.A=

 1 1 -2 3

SO,  A-1=
 Adj.A lAl
=
 1 5

 1 1 -2 3

=

 1/5 1/5 -2/5 3/5

Hence the inverse of the matrix =

 1/5 1/5 -2/5 3/5

(ii)

 -2 3 -4 5

Solution:

Let     A=

 -2 3 -4 5

Then A-1=
 Adj.A lAl
lAl=

 -2 3 -4 5

=-10+12 =2≠0
Adj.A=

 5 -3 4 -2

SO,  A-1=
 Adj.A lAl
=
 1 2

 5 -3 4 -2

=

 5/2 -3/2 4/2 -2/2

Hence the inverse of the matrix=

 5/2 -3/2 2 -1

(iii)

 2ι ι ι -ι

Solution:

Let     A=

 2ι ι ι -ι

Then A-1=
 Adj.A lAl
lAl=

 2ι ι ι -ι

=-2ι22 =-2(-1)-(-1)=2+1=3≠0
Adj.A=

 -ι -ι -ι 2ι

SO,  A-1=
 Adj.A lAl
=
 1 3

 -ι -ι -ι 2ι

=

 -ι/3 -ι/3 -ι/3 2ι/3

Hence the inverse of the matrix=

 -ι/3 -ι/3 -ι/3 2ι/3

(iv)

 2 1 6 3

Solution:

Let     A=

 2 1 6 3

Then A-1=
 Adj.A lAl
Adj.A=

 1 1 -2 3

lAl=

 2 1 6 3

=6-6 =0

Hence , the inverse cannot be determined.

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