Fsc Part 1 Mathematics (Complete Solution)

# Q12 Find the matrix x if;

(i)    X

 5 2 -2 1

=

 -1 5 12 3

Solution:

X

 5 2 -2 1

=

 -1 5 12 3

Let  X=

 a b c d

then

 a b c d

 5 2 -2 1

=

 -1 5 12 3

 5a-2b 2a+b 5c-2d 2c+d

=

 -1 5 12 3

Comparing the corresponding elements, we get

5a-2b=-1   ...............(i)

2a+b=5     ...............(ii)

5c-2d=12   ................(iii)

2c+d=3      ................(iv)

to solve (i) and (ii), put b=5-2a from (ii) in(i) then

5a-2(5-2a)=-1

5a-10+4a=-1

9a=9

=> a=1

put a=-1 in(ii) , then

b=5-2a

b=5-2(1)

b=5-2

b=3

to solve (iii) and (iv), put d=3-2c from (iv) in (iii), then

5c-2(3-2c)=12

5c-6+4c=12

9c=18

c=2

put c=2 in (iv) , then

d=3-2c=5-2(2)=3-4=-1

d=-1

Thus    X=

 a b c d

=

 1 3 2 -1

(ii)

 5 2 -2 1

X=

 2 1 5 10

Solution:

 5 2 -2 1

X =

 2 1 5 10

Let  X=

 a b c d

then

 5 2 -2 1

 a b c d

=

 2 1 5 10

 5a-2c 5b+2d -2a+c -2b+d

=

 2 1 5 10

Comparing the corresponding elements, we get

5a+2c=2  ...............(i)

5b+2d=1    ...............(ii)

-2a+c=5   ................(iii)

-2b+d=10      ................(iv)

to solve (i) and (iii), put c=5+2a from (iii) in (i) , then

5a+2(5+2a)=2

=> 5a+10+4a=2

9a=-8

a=-8/9

put a=-8/9   in (iii) , then

c=5+2a

c=5+2(-8/9)

c=29/9

to solve (ii) and (iv) , put d=10+2b from (iv) in (ii), then

5b+2(10+2b)=1

=> 5b+20+4b=1

9b=-19

b=-19/9

put b=-19/9  in (ii), then

d=10+2b

d=10+2(-19/9)

d=10-38/9

d=52/9

Thus    X=

 a b c d

=

 -8/9 -19/9 29/9 52/9