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Applications of the Matrix Inverse Method

Applications of the Matrix Inverse Method. Real-life problems often involve solving for a large number of variables. The Matrix Inverse Method turns out to be usually more efficient than the methods of substitution and elimination.

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Applications of the Matrix Inverse Method

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  1. Applications of the Matrix Inverse Method

  2. Real-life problems often involve solving for a large number of variables. • The Matrix Inverse Method turns out to be usually more efficient than the methods of substitution and elimination. • The graphical method does not apply when there are more than 2 variables

  3. As always, the first step is to set up a mathematical representation of the given real-life problem.

  4. How many unknowns are there? • Define them as variables. • Organize the given information on a table

  5. Obtain a system of linear equations • Apply the Matrix Inverse Method. • Interpret the results. 20 cases of orange juice, 12 cases of tomato juice, and 6 cases of pineapple juice are prepared.

  6. We now apply the matrix inverse method to solve a puzzle

  7. There are 20 nickels, 50 dimes, and 10 quarters. Hence, there are 80 coins.

  8. One of the major advantages of the matrix inverse method: • When we make minor changes to a system, there is no need to start from scratch to solve the new system.

  9. a) • Invest $4,000, $1,000, and $5,000 at 6%, 7%, and 8%, respectively. • Invest $2,500, $2,500, and $5,000 at 6%, 7%, and 8%, respectively. • Just invest $5,000 at 7% and $5,000 at 8%, respectively. • There is no way of meeting the person’s investment requirements for a return of $775. b) At least $700 and at most $750.

  10. The Matrix Inverse Method is not a cure for all ills • Some limitations: • It is used only when the coefficient matrix is a square matrix • It is used only when the coefficient matrix has an inverse

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