Solving Systems of Equations using a Matrix Method
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 22 carbohydrates and 14 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 to receive full credit.
Carbohydrates Protein
Peanut Butter 2 4
Oats 8 1
A. Write an equation for the total amount of carbohydrates.
B. Write an equation for the total amount of protein.
C. Determine the augmented matrix that represents the previous two equations.
D. Solve for the previous matrix. Show all work to receive full credit.
E. How many tablespoons of each will there need to be for the new energy bar?
A system of equations is subjected to matrix methods .
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- Linear Algebra : Matrix Proof - Prove that if ; A is a 2x2 matrix then A2-Tr(A)A+Det(A)I=0.
- Symmetric Matrix - Please see the attached file for the fully formatted problems.
- Eigenvectors - Show that the matrix reduces the given matrix to the diagonal form by the transformation i.e., diagonal matrix.
- Augmented Matrix - Write the augmented matrix of the given system. *(Please see attachment for system)
- Diagonalizability - Show that the matrix reduces the given matrix to the diagonal form by the transformation i.e., diagonal matrix.
