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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1Suppose P is the invertible and A = PBP^-1. Solve for B in terms of A.Consider the ODE eigenvalue problem: ((1-x2)1/2φ')' + λ(1-x2)-1/2φ = 0 posed for -1 < x < 1 and subject to the boundary condidiont |φ(-1)| < ∞ and |φ(1)| < ∞. If you find it helpful you, you may assume |φ'(-1)| < ∞ and |φ'(1)| < ∞. a) Show that this is a Sturm-Liouville eigenvalue problem, i.e, verify that it has the correct form and identify the coefficients p, q, and σ. Is the problem regular? Why or why not? b) Show that λ > 0 for each eigenvalue λ.
- only question 12 question about:THE S + N DECOMPOSITIONA and B each have certain number of oranges. A says to B if you give me 10 of your oranges i will have the twice the number of oranges left with you. B replies if you give me 10 oranges i will have the same number of oranges as left with you find the number of oranges with A and B seperatelyThe matrix A=[7 k] [-8 −4] has two distinct real eigenvalues if and only if k<_____ (Find the value that makes this statement true).