1. Matrix problem.

Hello guys, this my first topic here, and I hope I'm putting this in the correct place. I have a bit of a problem with a matrix question I was asked to solve,

Julia is preparing a meal by combining three ingredients. One unit of each ingredient provides the following quantities (in grams) of carbohydrates, fat, and protein.

Protein(g) Carbohydrates(g) Fat (g)
Ingredient A 3 3 1
Ingredient B 2 4 2
Ingredient C 4 5 1

Ideally the meal should contain 26 grams of protein, 34 grams of carbohydrates, and 12 grams of fat. How many units of each ingredient should Julia use?

I'm actually at total loss as to what I should do here. I can solve systems of equations with no issues, but this is just messing with my mind. I am not very good at math, so any help would be appreciated.

2. Re: Matrix problem.

Let a, b and c be the numbers of units of ingredients A, B and C, respectively. Then 3a + 2b + 4c = 26 and similarly for carbohydrates and fat. If you know matrix multiplication, the problem is to find the vector (a, b, c) such that

$\begin{pmatrix}a&b&c\end{pmatrix} \begin{pmatrix}3&3&1\\2&4&2\\4&5&1\end{pmatrix} = \begin{pmatrix}26&34&12\end{pmatrix}$

3. Re: Matrix problem.

Wow! I got the answer! It was A = 4, B = 3 and C = 2! Thanks very much for the help!