Fsc Part 1 Mathematics (Complete Solution)

# Q13 Find the matrix a if ,

(i)

 5 -1 0 0 3 1

A=

 3 -7 0 0 7 2

Solution:

 5 2 -2 1

A =

 2 1 5 10

Let  A=

 a b c d

then

 5 -1 0 0 3 1

 a b c d

=

 3 -7 0 0 7 2

 5a-c 5b-d 0+0 0+0 3a+c 3b+d

=

 3 -7 0 0 7 2

Comparing the corresponding elements, we get

5a-c=3 ......(i)

5b-d=-7 ......(ii)

3a+c=7    .....(iii)

3b+d=2  ........(iv)

adding (i) and (iii), we get

8a=10

=> a=5/4

(iii) gives c=7-3a

=7-15/4

c=13/4

adding (ii) and (iv) , we get

8b=-5

b=-5/8

(iv) gives d=2-3b

d=2+15/8

d=31/8

Thus    A=

 a b c d

=

 5/4 -5/8 13/4 31/8

(ii)

 2 -1 -1 2

A=

 0 -3 8 3 3 -7

Solution:

 2 -1 -1 2

A =

 0 -3 8 3 3 -7

Let  A=

 a b c d e f

then

 2 -1 -1 2

 a b c d e f

=

 0 -3 8 3 3 -7

 2a-d 2b-e 2c-f -a+2d -b+2e -c+2f

=

 0 -3 8 3 3 -7

Comparing the corresponding elements, we get

2a-d=0 .........(i)

2b-e=-3  ..........(ii)

2c-f=8 .........(iii)

-a+2d=3 ...............(iv)

-b+2e=3   ................(v)

-c+2f=-7 ........(vi)

To solve (i) and (iv) , put d=2a from (i) in (iv) , then

-a+2d=3

-a+2(2a)=3

-a+4a=3

3a=3

a=1

put a=1 in (iv), then

d=2a

d=2(1)

d=2

to solve (ii) and (v) , put e=2b+3 from (ii) in (v), then

-b+2(2b+3)=3

-b+4b+6=3

3b=-3

b=-1

put b=-1 in (v) , then

e=2b+3

e=2(-1)+3

e=-2+3

e=1

to solve (iii) and (vi), put f=2c-8 from (iii) in (vi), then

-c+2f=-7

-c+2(2c-8)=-7

3c=9

c=3

put c=3 in (vi) , then

f=2c-8

f=2(3)-8

f=6-8

f=-2

Thus    A=

 a b c d e f

=

 1 -1 3 2 1 -2