How to Use Gaussian Elimination to Solve for Vitamin Pills

Thread starter sdoug041
Start date Jan 15, 2010
Tags

Algebra Linear Linear algebra

In summary: A, you get 8 units of vitamin B, and for every 0 unit of vitamin A, you get 1 unit of vitamin C. However, because there are no pills in brand 3, the coefficient for that brand is 0.

Jan 17, 2010

memomator

Thank you very much Dick, I finally understand. You have 6 solutions. Because B3 is between 3 and 8 and the numbers between 3 and 8 are solutions and you take those number and sub them into the other equation to find out b1 and b2.

<h2>1. What is Gaussian Elimination and how does it work?</h2><p>Gaussian Elimination is a method used to solve systems of linear equations. It involves manipulating the equations through row operations to eliminate variables and eventually solve for the remaining variables. This is done by converting the equations into an augmented matrix and then using elementary row operations to reduce the matrix into its row echelon form.</p><h2>2. Can Gaussian Elimination be used to solve for vitamin pills?</h2><p>Yes, Gaussian Elimination can be used to solve for any set of linear equations, including those related to vitamin pills. The method remains the same, but the equations will involve the amounts of different vitamins in each pill and the recommended daily intake of each vitamin.</p><h2>3. What are the steps involved in using Gaussian Elimination to solve for vitamin pills?</h2><p>The steps involved in using Gaussian Elimination to solve for vitamin pills are:<ol><li>Write out the system of equations representing the vitamin pills.</li><li>Convert the equations into an augmented matrix.</li><li>Use elementary row operations to reduce the matrix into its row echelon form.</li><li>Use back substitution to solve for the remaining variables.</li><li>Check the solution by substituting the values back into the original equations.</li></ol></p><h2>4. Are there any limitations to using Gaussian Elimination to solve for vitamin pills?</h2><p>One limitation of Gaussian Elimination is that it can only be used to solve for linear equations. If the equations representing the vitamin pills are non-linear, then another method, such as substitution or elimination, would need to be used. Additionally, if the system of equations is inconsistent or has infinitely many solutions, then Gaussian Elimination may not provide a unique solution.</p><h2>5. How can Gaussian Elimination be applied to real-life situations involving vitamin pills?</h2><p>Gaussian Elimination can be applied to real-life situations involving vitamin pills by using the system of equations to determine the optimal combination of pills to meet the recommended daily intake of each vitamin. It can also be used to compare different brands of vitamin pills and their compositions to determine which one best meets an individual's vitamin needs.</p>

1. What is Gaussian Elimination and how does it work?

Gaussian Elimination is a method used to solve systems of linear equations. It involves manipulating the equations through row operations to eliminate variables and eventually solve for the remaining variables. This is done by converting the equations into an augmented matrix and then using elementary row operations to reduce the matrix into its row echelon form.

2. Can Gaussian Elimination be used to solve for vitamin pills?

Yes, Gaussian Elimination can be used to solve for any set of linear equations, including those related to vitamin pills. The method remains the same, but the equations will involve the amounts of different vitamins in each pill and the recommended daily intake of each vitamin.

3. What are the steps involved in using Gaussian Elimination to solve for vitamin pills?

The steps involved in using Gaussian Elimination to solve for vitamin pills are:

Write out the system of equations representing the vitamin pills.
Convert the equations into an augmented matrix.
Use elementary row operations to reduce the matrix into its row echelon form.
Use back substitution to solve for the remaining variables.
Check the solution by substituting the values back into the original equations.

4. Are there any limitations to using Gaussian Elimination to solve for vitamin pills?

One limitation of Gaussian Elimination is that it can only be used to solve for linear equations. If the equations representing the vitamin pills are non-linear, then another method, such as substitution or elimination, would need to be used. Additionally, if the system of equations is inconsistent or has infinitely many solutions, then Gaussian Elimination may not provide a unique solution.

5. How can Gaussian Elimination be applied to real-life situations involving vitamin pills?

Gaussian Elimination can be applied to real-life situations involving vitamin pills by using the system of equations to determine the optimal combination of pills to meet the recommended daily intake of each vitamin. It can also be used to compare different brands of vitamin pills and their compositions to determine which one best meets an individual's vitamin needs.