SOLUTION: Find three numbers whose sum is 32;, if the first number is three times the difference between the second and the third, and the second number is two more than twice the third. Sol

Algebra ->  Matrices-and-determiminant -> SOLUTION: Find three numbers whose sum is 32;, if the first number is three times the difference between the second and the third, and the second number is two more than twice the third. Sol      Log On


   

Question 1115173: Find three numbers whose sum is 32;, if the first number is three times the difference between the second and the third, and the second number is two more than twice the third. Solve the problem using matrices.
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
first number      3(2n+2-n)=3(n+2)
second number     2n+2
third number       n

One single equation in variable n.
3%28n%2B2%29%2B%282n%2B2%29%2Bn=32
Solve and evaluate firstnumber and secondnumber.

The problem seems not to really benefit from using matrices.

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If really matrix is wanted, then first second third numbers can be x, y, z.
Description could be system of equations:
system%28x%2By%2Bz=32%2Cx-3y%2B3z=0%2Cy-2z=2%29

Corresponding starting matrix would be
matrix%283%2C4%2C%0D%0A1%2C1%2C1%2C32%2C%0D%0A1%2C-3%2C3%2C0%2C%0D%0A0%2C1%2C-2%2C2%29