For Exercises 72-73, use a graphing calculator and the inverse of the coefficient matrix to find the solution to the given system. Round to 2 decimal places.
72.
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College Algebra & Trigonometry Special Edition For Washington State University Pullman
- 7. A substance N1 decays with a half-life of 45 seconds to substance N2. N2 has a half-life of 5 minutes and decays to the stable substance N3. Model the system (but do not solve the equations) if initially, there are 40 grams of N1, 20 grams of N2, and 12 grams of N3.arrow_forwardHow do you calculate when the matrix is equal to 0 ?arrow_forwardHow much longer should you expect Gaussian elimination to work on a system of 1000 equations versus a system of 500 equations?arrow_forward
- Solve the following nonhomogeneous system of linear differential equations.You can use Mathcad, Excel, a calculator, or hand calculations for the required matrix calculationsarrow_forwardto show why (e^(At))=the shown matrix, write the matrix exponential (as an infinite sum) for the system of differential equations given in matrix form for the first coefficient matrix.arrow_forwardsolve th e given system x- y=1 ,2x+y =2arrow_forward
- In Exercises 7-10, find a linear equation that has the same solution set as the given equation (possibly with some restrictions on the variables). 10.arrow_forwardIn Exercises 20-23, solve the given matrix equation for X. Simplify your answers as much as possible. (In the words of Albert Einstein, Everything should be made as simple as possible, but not simpler.) Assume that all matrices are invertible. XA2=A1arrow_forwardRedo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?arrow_forward
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