Using matrices to solve systems,2 questions, pre-calc. help?

[anony]

1.) Solve for a and b. With work.

[a b] [2 0] = [8 -8]
........[1 -1]
**Ignore dots and pretend brackets are conjoined where they would be normally**

2.) A company's employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 31 carbohydrates and 23 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. Show all work.

Carbohydrates ...... Protein

Peanut Butter 2.........6

Oats 5.......................1

**ignore the dots, the table is weird looking here, i know. Peanut butter has 2 carbs and 6 grams of protein while oats has 5 carbs and 1 gram of protein.**

Thank you in advance for the help!

 

[Deleted member 4993]

1.) Solve for a and b. With work.

[a b] [2 0] = [8 -8]
........[1 -1]
**Ignore dots and pretend brackets are conjoined where they would be normally**

2.) A company's employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 31 carbohydrates and 23 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. Show all work.

Carbohydrates ...... Protein

Peanut Butter 2.........6

Oats 5.......................1

**ignore the dots, the table is weird looking here, i know. Peanut butter has 2 carbs and 6 grams of protein while oats has 5 carbs and 1 gram of protein.**

Thank you in advance for the help!

What method have you been taught?

Matrix inversion?

Cramer's rule?

Gauss-Jordan elimination?

Please share your work with us ...

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[stapel]

1.) Solve for a and b. With work.

[a b] [2 0] = [8 -8]
........[1 -1]
**Ignore dots and pretend brackets are conjoined where they would be normally**

You might find "code" tags to be helpful for matrix multiplication. I think you mean this:

[a b][2  0] = [8 -8]
     [1 -1]

If so, what did you get when you did the matrix multiplication on the left-hand side?

2.) A company's employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 31 carbohydrates and 23 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices.

What variables did you pick? How did you define them? What equations did you create?

Please be complete. Thank you!