College algebra
posted by YANETH on .
system of linear equation
The sum of 3 numbers is 14
the largest is 4 times the smallest
the sum of the smallest and twice the largest is 18
what are the 3 numbers? show work?
A. how many unknowns you have?
how many equations need to be solve for that many unknown?
B. what are the equations?
C. used the system of equations using matrices.

x+y+z=14
z=4x
x+2z=18
=================
x+y+4x = 14 or 5x+y = 14
x+8x = 18
or x = 2
so
y = 14  10 = 4
z = 4*2=8
3 unknowns, three equations
I did it with substitution, however can form augmented matrix and use Gauss Jordan:
+1 1 1 14
4 0 1 0
+1 0 2 18
then plug and chug 
post it.

matix solution
1 1 1  [x y z]'= [14 0 18]'
4 0 1 
1 0 2 
H*[x y z]' = [14 0 18]' (' stands for transpose; in this case makes row vector a column vector)
Answer
inv(H)*H*[x y z]'= inv(H)*[14 0 18]'
[x y z] = inv(H)*[14 0 18]'
inverting a 3x3 matrix
inv(H)=1/H*adj(H) H=det(H)
adj(H)=
+(00) (81) +(00)'
(20) (21) (01)
+(10) (1+4) +(0+4)
0 9 0'
2 1 1
1 5 4
=0 2 1
9 1 5
0 1 4
det(H)= use the second column
since it has 2 zeros it makes
it easy.
det(H)=1(81)+0*(21)0*(1+4)=9
inv(H)=1/9*0 2 1
9 1 5
0 1 4
[x y z]'= inv(H)*[14 0 18]'
=[18/9 (9*145*18)/9 (18*4)/9]'
=[ 2 4 8 ]'
hope this helps