Find a generalized eigenvector of a

Reference no: EM13910339

1. Let

a. The matrix A only has one eigenvalue. Find it and and an eigenvector of A.

b. Find a generalized eigenvector of A.

c. Solve the Initial Value Problem below.

d. Classify the phase portrait.

2. Consider two interconnecting tanks. Tank 1 initially contains 750 L (liters) of water and 200 g of sugar, while Tank 2 initially contains 250 L of water and 100 g of sugar. Water containing 5 g/L of sugar is poured into Tank 1 at a rate of 40 L/m while the mixture flowing into Tank 2 contains a sugar concentration of 3 g/L and is flowing at a rate of 15 L/min. The mixture flows from Tank 1 to Tank 2 at a rate of 40 L/min. The mixture drains from Tank 2 at a rate of 50 L/min, of which some flows back into Tank 1 at a rate of 15 L/min, while the remainder leaves the tank. Let x and y, respectively, be the amount of sugar in each tank at time t. Set up BUT DO NOT SOLVE an initial value problem that models the flow process.

Reference no: EM13910339

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