Hey, I am very new at using matrices to solve systems of equations. My question isnt actually how to invert a matrix or anything, its much simpler.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

If you add the age of 6 people, Anna, Barbara, Cathy, Dan, Eric, Fred, the total is 92. Anna is twice the age of Cathy. The total age of Barbara and Eric equals that of Fred. The total age of Anna and Cathy equals the total age of Barbara and Fred. Cathy is 8 years younger than Fred. If you subtract the age of Eric and Cathy from Dan the result is 10.

What is the age of each person?

2. Relevant equations

I need to write a linear equation for each of the above conditions and then convert the equations into matrices of form Ax=b.

Then I need to write a program that will solve the matrices for the unknowns. You see I don't have to solve the matrices myself, my program will do that for me. And besides once I can write out the matrices, I know what to do.

What I can't seem to do is construct appropriate linear equations from the above conditions. Here is what I tried. This is the best I can do so far.

3. The attempt at a solution

Each letter stands for the name of the person, A = Anna and etc.

A+B+C+D+E+F = 92

A= 2C

B+E=F

A+C= B+F

F-8= C

E+C-D = 10

Here I have 6 linear equations (I think), and 6 unknowns. Meaning 6 by 6 matrix. But what are the coefficients that I put in the matrix? They look like mostly 1's. This can't be right. Help me out please.

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# Homework Help: Simple systems of linear equations question

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