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In Exercises 1 and 2, let A = PDP−1 and compute A4.
1. P =
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Linear Algebra and Its Applications (5th Edition)
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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 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 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2arrow_forwardProve the half of Theorem 3.3 (e) that was not proved in the text.arrow_forwardLet A [ - 5 13 12 13 2333 12 13 5 Explain why A-₁ = AT. -1 13arrow_forward
- At the Blood Bank, they know that O+blood is the most common blood type and that 40% of the people are known to have 0+blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X = number of people who have blood type O+ Y = number of people who have blood type A- Z = number of people who have blood type A or B a) Consider a random sample of n = 12 people who donated blood over the past three months. The expected number of people with blood type O+is and the expected number of people with blood type A-is Round your answers to 2 decimal places. Calculate the following probabilities: P(X = 9) Round your answer to 4 decimal places. o P(X > 3) = Round your answer to 4 decimal places.arrow_forwardAt the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B Consider a random sample of n=9 people who donated blood over the past three months. a) The expected number of people with blood type O+ is _____and the expected number of people with blood type A- is ______Round your answers to 2 decimal places. b) Calculate the following probabilities: P(X=5)=_________ Round your answer to 4 decimal places. P(X>2)=_________ Round your answer to 4 decimal places.arrow_forwardAt the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B a) Consider a random sample of n=9 people who donated blood over the past three months. The expected number of people with blood type O+ is and the expected number of people with blood type A- is Calculate the following probabilities: P(X=5)= __________ Round your answer to 4 decimal places. P(X>2)= __________ Round your answer to 4 decimal places. b) Consider a random sample of n=40 people who donated blood over the past three months. Use the relevant probability function of Y to calculate the probability that 2 people in the random sample will have type A- blood. ________…arrow_forward
- At the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B please answer a) b) and c)arrow_forwardIf u = x1x2 + x2x3+ X3X1, then find the relative percentage error in the computation of u at x1 = 2.104, x2 1.935 and x3= = 0.845.arrow_forwardFind all numbers z such that Az3 + Bz² + Cz = D %3D B = [2 4 21 1. A = 1 1 -2 -1 1 3 1. 1 2 4 21 C li 3 D = [4 -1 1arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
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