By adding first and third numbers, we get double of the
second number Represent it algebraically and find the numbers using matrix method Solution Let first, second and third numbers be denoted by x, y and z, respectively Then, according to given conditions, we have
x + y + z = 6
y + 3z = 11
x + z = 2y  or x – 2y + z = 0
This system can be written as A X = B, where
A =  
1
1
1
0
1
3
1
2
1
�








, X = 
x
y
z








 and B = 
6
11
0








Here 
(
)
(
)
A
1 1
6 – (0 – 3)
0 –1
9
0
=
+
+
=
≠