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Question

The sum of three numbers is 6 when second number is subtracted from thrice the sum of first and third number, we get numbers 10. Four times the third number is subtracted from five times the sum of first and second number, the result is 3. Using above information, find these three numbers by matrix method.

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Solution

Let the numbers be x,y and z

According to question, x+y+z=6 ...... (i)

3(x+z)y=10

or 3xy+3z=10 ........ (ii)

Also, 5(x+y)4z=3

or 5x+5y4z=3 ........ (iii)

Thus, xyz111313554=6103

Applying R3R35R1

xyz111313009=61027

Thus, the equations reduce to

x+y+z=6 ..... (iv)

3xy+3z=10 ..... (v)

9z=27z=3 .... (vi)

Adding (iv) and (v), we get

4x+4z=16x+z=4 ..... (vii)

Substitute value of z from (vi) in (vii),

x+3=4x=1

Substitute the values of x and z in (iv), we get

1+y+3=6y=2

Hence, the numbers are 1,2 and 3.

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